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

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

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

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

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

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

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

    <p>True</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%</p> Signup and view all the answers

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

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

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

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

    Rules of inference help draw conclusions from given premises.

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

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

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

    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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    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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