Propositions and Logical Operators Quiz
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Questions and Answers

What is the future value of the annuity in the first example?

  • ₱37,900.06
  • ₱21,000.00
  • ₱150,000.00
  • ₱156,612.59 (correct)

The present value of the annuity in the first example is ₱150,000.

False (B)

What is the cash price of the vacant lot based on the down payment and annuity?

₱324,434.70

The present value of an annuity due is the sum of the __________ of the periodic payments.

<p>present values</p> Signup and view all the answers

In the example, how often are payments made?

<p>Semiannually (C)</p> Signup and view all the answers

Match the following terms with their definitions:

<p>Present Value = The current worth of future cash flows Future Value = The value of an investment after earning interest Annuity = A series of equal payments made at regular intervals Cash Price = The total amount paid upfront for an item</p> Signup and view all the answers

The interest rate used in the example is 3%.

<p>False (B)</p> Signup and view all the answers

What is the value of 'i' used in the example where the cash price of the lot is calculated?

<p>0.05</p> Signup and view all the answers

What is the approximate Yield to Maturity calculated in the solution?

<p>4.04% (C)</p> Signup and view all the answers

The Theory of Efficient Markets suggests that future stock prices can be easily predicted.

<p>False (B)</p> Signup and view all the answers

What is the calculation used to determine the interest income in the solution?

<p>₱300</p> Signup and view all the answers

The weak form of the Efficient Market Hypothesis assumes that current stock prices reflect all __________ information.

<p>historical</p> Signup and view all the answers

Which sub-theory of the Efficient Market Hypothesis assumes that stock prices reflect insider information?

<p>Strong form (D)</p> Signup and view all the answers

What is the formula used to calculate time (t) in simple interest?

<p>t = I / (P * r) (B)</p> Signup and view all the answers

Match the forms of the Efficient Market Hypothesis with their definitions:

<p>Weak form = Current prices reflect all historical information Semi-strong form = Current prices reflect all historical and publicly available information Strong form = Current prices reflect historical, publicly available, and insider information</p> Signup and view all the answers

Exact interest is computed based on a year ratio of 1 year to 360 days.

<p>False (B)</p> Signup and view all the answers

According to the semi-strong form of market efficiency, which type of analysis is least beneficial to investors?

<p>Fundamental analysis (C)</p> Signup and view all the answers

What is the total cash flow (C) given in the solution?

<p>₱6,480</p> Signup and view all the answers

How many days did it take Miss Uy to repay the loan?

<p>270</p> Signup and view all the answers

Mr. Sandoval paid exactly ₱1,200 interest at 8% for _____ days.

<p>146</p> Signup and view all the answers

Which ratio is used for calculating ordinary interest?

<p>1 year : 360 days (A)</p> Signup and view all the answers

What amount did Miss Uy borrow from the bank?

<p>₱80,000</p> Signup and view all the answers

₱5,400 earned on a principal of ₱80,000 at an interest rate of _____ percent.

<p>9</p> Signup and view all the answers

What is the total cost calculated from the expenses given?

<p>₱9,733.50 (D)</p> Signup and view all the answers

The net gain is calculated as total received minus total cost.

<p>True (A)</p> Signup and view all the answers

What is the total dividend received if each share provides ₱1 and there are 525 shares?

<p>₱525</p> Signup and view all the answers

The rate of return is calculated using the formula: Total gains divided by _____ cost.

<p>Total</p> Signup and view all the answers

What is the approximate yield to maturity if: annual interest (I) is ₱420, par value (P) is ₱7,000, cost (C) is ₱6,650, and n is 5?

<p>6.88% (B)</p> Signup and view all the answers

The current yield is calculated using the price per share instead of the cost.

<p>True (A)</p> Signup and view all the answers

What is the gain calculated from the total received minus the total cost?

<p>₱1,622.25</p> Signup and view all the answers

What type of proposition is 𝑃𝑃 ∨ (∼ 𝑃𝑃)?

<p>Tautology (A)</p> Signup and view all the answers

The expression 𝑄𝑄 ∧ (∼ 𝑄𝑄) is a tautology.

<p>False (B)</p> Signup and view all the answers

Is the proposition 𝑃𝑃 ∨ (∼ 𝑄𝑄) a tautology, contradiction, or neither?

<p>neither</p> Signup and view all the answers

The proposition (𝑃𝑃 ∨ 𝑄𝑄) ∧ [(∼ 𝑃𝑃) ∧ (∼ 𝑄𝑄)] is a __________.

<p>contradiction</p> Signup and view all the answers

Match the compound propositions with their classifications:

<p>𝑃𝑃 ∨ (∼ 𝑃𝑃) = Tautology 𝑄𝑄 ∧ (∼ 𝑄𝑄) = Contradiction 𝑃𝑃 ∨ (∼ 𝑄𝑄) = Neither (𝑃𝑃 ∨ 𝑄𝑄) ∧ [(∼ 𝑃𝑃) ∧ (∼ 𝑄𝑄)] = Contradiction</p> Signup and view all the answers

Which of the following propositions is a contradiction?

<p>𝑄𝑄 ∧ (∼ 𝑄𝑄) (A)</p> Signup and view all the answers

Rules of inference help draw conclusions from given premises.

<p>True (A)</p> Signup and view all the answers

What is a syllogism?

<p>A form of reasoning in which a conclusion is drawn from two or more premises.</p> Signup and view all the answers

What is the primary conclusion of the argument 'If Q is the consequence of P, and Q did not happen, then P does not happen'?

<p>P does not happen (A)</p> Signup and view all the answers

All dolphins are mammals, therefore all mammals have kidneys, is an example of a syllogism.

<p>True (A)</p> Signup and view all the answers

Identify the fallacy in the statement: 'In a class of 50 students, 35 receive a daily allowance worth above P100. Hence, all 50 students receive allowance above P100.'

<p>fallacy of composition</p> Signup and view all the answers

The rule of inference that states 'If P implies Q and P is true, then Q must also be true' is known as __________.

<p>Modus Ponens</p> Signup and view all the answers

Which fallacy is characterized by failing to provide a logical connection between the premise and conclusion, appealing instead to emotion?

<p>Fallacy of relevance (C)</p> Signup and view all the answers

Provide an example of a syllogism.

<p>All humans are mortal; Socrates is a human; therefore, Socrates is mortal.</p> Signup and view all the answers

Match the following fallacies with their definitions:

<p>Fallacy of Composition = Attributing to the whole what is observed in part Fallacy of Relevance = Failing to connect premises and conclusions logically Syllogism = A form of reasoning where a conclusion follows logically from premises Fallacy of Hasty Generalization = Jumping to conclusions based on insufficient evidence</p> Signup and view all the answers

The classmate who borrowed my pen is my only classmate without a pen. Who is the borrower?

<p>Mike (B)</p> Signup and view all the answers

Flashcards

Exact Interest

Simple interest calculated based on a 365-day year.

Ordinary Interest

Simple interest calculated based on a 360-day year.

Principal

The amount of money borrowed or lent.

Interest Rate (r)

The annual rate of interest charged on the borrowed amount.

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Time (t)

The length of time for which the money is borrowed or lent.

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Interest (I)

The total interest earned or paid over the life of the loan or investment.

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Simple Interest Formula (I = Prt)

The formula used to calculate simple interest for a given principal, interest rate, and time period.

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Converting Time to Days

The process of converting a time period expressed in years to days, using either a 365-day (exact) or 360-day (ordinary) year.

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Bond Yield

The ratio of annual dividend to price per share. Represents the return on investment in a bond, expressed as a percentage.

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Current Yield

The ratio of annual dividend to the current market price of the bond. Reflects the current return on the bond.

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Approximate Yield to Maturity (YTM)

An estimate of the total return an investor can expect to receive from holding a bond until maturity, considering both interest payments and capital appreciation.

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Rate of Return

The total return received from investing in a bond, including both interest payments and any capital gains or losses.

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Annual Dividend (Bond)

The annual interest payment a bondholder receives from the issuer.

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Par Value (Bond)

The face value of a bond, which is the amount the issuer promises to pay back to the bondholder at maturity.

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Current Price (Bond)

The price at which a bond is currently trading in the market.

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Years to Maturity

The number of years remaining until the bond reaches its maturity date.

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Present Value of an Annuity (PVA)

The total amount of money that would be needed today to have the same value as a series of future payments, taking into account the time value of money.

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Future Value of an Annuity (FVA)

The total amount of money that a series of future payments would accumulate to at the end of the term, considering interest earned.

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Present Value of an Annuity Due (PVADue)

The present value of a series of future payments, where each payment is received or made at the beginning of each period.

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Future Value of an Annuity Due (FVADue)

The future value of a series of future payments, where each payment is received or made at the beginning of each period.

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Equivalent Cash Price

The difference between the purchase price of an asset and the down payment. Calculated as the present value of the remaining payments.

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Time Value of Money

The time value of money concept that states that a sum of money today is worth more than the same sum of money in the future, due to its potential to earn interest or grow.

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Weak Form of Efficient Market Theory

The assumption that current stock prices reflect all historical information, including past returns. This means that technical analysis, which studies stock price charts to predict future movements, is unlikely to be effective.

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Semi-Strong Form of Efficient Market Theory

The assumption that stock prices already reflect all publicly available information, including historical data and current news. Hence, fundamental analysis, where investors analyze company financials, is unlikely to produce superior returns.

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Strong Form of Efficient Market Theory

The assumption that stock prices incorporate all information, including insider information. Consequently, no investor can consistently earn above-average returns because all information is already reflected in the prices.

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Fundamental Analysis

The process of analyzing a company's financial statements and recent developments to assess its value and potential for future growth. This can involve looking at things like revenue, earnings, debt, and assets.

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Technical Analysis

The practice of studying stock price charts, patterns, and trends to identify potential buying and selling opportunities. Technical analysts look for signals in the price movement to predict future price changes.

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Theory of Efficient Markets

The belief that stock prices accurately reflect all available information. This means that it's impossible to consistently beat the market by predicting future price movements.

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Yield to Maturity

The annual percentage rate of return that an investor expects to earn on a bond or other debt security if they hold it until maturity. It's an estimation of the total return, taking into account interest income and capital gains or losses.

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Beta

A measure of how closely the price of a security moves relative to the market as a whole. It can indicate how volatile or stable the security is compared to the overall market.

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Tautology

A proposition that is always true, regardless of the truth values of its variables.

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Contradiction

A proposition that is always false, regardless of the truth values of its variables.

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Neither a Tautology nor a Contradiction

A proposition that can be either true or false, depending on the truth values of its variables.

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Rules of Inference

A logical argument that uses rules to draw a valid conclusion from one or more premises.

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Syllogism

A logical argument that uses rules to reach a conclusion based on two or more premises.

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Consequence

A statement that expresses a relationship or connection between two elements. For example, if P happens, then Q will happen.

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Premise

A statement that expresses a condition or requirement that must be met. For example, if P is true, then Q must also be true.

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Truth Tables

The process of determining the truth value of a compound proposition based on the truth values of its components.

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Valid Argument

A logical argument where the conclusion is always true if the premises are also true.

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Invalid Argument

A logical argument where the conclusion doesn't necessarily follow from the premises, even if the premises are true.

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Modus Ponens

A rule of inference where if a statement and its implication are true, then the conclusion must also be true. Example: If P, then Q. P is true, therefore Q is true.

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Modus Tollens

A rule of inference where if a statement and its negation are true, then the antecedent must be false. Example: If P, then Q. Q is false, therefore P is false.

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Fallacy

An erroneous argument that lacks logical connection between the premise and the conclusion.

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Fallacy of Composition

A fallacy where a conclusion about a whole group is drawn from a single instance or a small sample.

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Fallacy of Relevance

A fallacy where the argument relies more on emotions and irrelevant appeals rather than logical reasoning and facts.

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Study Notes

Propositions

  • A proposition is a declarative statement that can be evaluated as either true or false.
  • A simple proposition contains one declarative sentence.
  • A compound proposition consists of two or more simple propositions connected by logical operators.

Logical Operators

  • Logical operators connect propositions to create new compound propositions or modify existing ones.

  • Conjunction: Uses "and" to connect statements.

    • A conjunction is TRUE only if both components are TRUE.

  • Disjunction: Uses "or" to connect statements.

    • A disjunction is FALSE only if both components are FALSE.

  • Implication: Uses "if-then" to connect statements.

    • The statement after "if" is called the premise. The statement after "then" is the conclusion.
    • An implication is FALSE only if the premise is TRUE and the conclusion is FALSE.

  • Biconditional: Uses "if and only if" or is equivalent to" to connect statements.

    • A biconditional statement is TRUE if both parts have the same truth value.

  • Negation: Uses "not" to modify a statement.

    • A negation is TRUE when the original proposition is FALSE.

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Simple Interest GenMath PDF

Description

Test your understanding of propositions and logical operators. This quiz covers the definitions of simple and compound propositions, as well as the main logical operators: conjunction, disjunction, implication, and biconditional. Sharpen your logical reasoning skills with this engaging quiz!

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