Proposition Quiz: Logic and Propositions Study Guide

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Questions and Answers

Which of the following statements is a proposition?

My seatmate will get a perfect score in the Logic exam. (correct)

Find a number which divides your age.

Mindanao is an island in the Philippines.

Welcome to the Philippines.

Which of the following statements is not a proposition?

$3 + 2 = 5$

What is the domain of the function. (correct)

$f(x) = x/(x+1)$ is a rational function.

$2x + 1 = 3$

From the given symbolic propositions, which one is false?

$\pi \notin \mathbb{Q}$ (correct)

$2 \in \mathbb{N}$

$-100 \in \mathbb{Z}$

$\pi \in \mathbb{R}$

Express the conjunction $p \land q$ as an English sentence.

p and q Signup and view all the answers

Which of the following statements is equivalent to $p \land (\sim q)$?

$\sim p$ but not $q$ Signup and view all the answers

Which of the following symbols best represents the conjunction of two propositions?

^ Signup and view all the answers

Which symbol is used to denote the disjunction operator?

∨ Signup and view all the answers

In the context of logic, what is a disjunction?

A logical operator used to connect two or more propositional statements with the meaning 'or'. Signup and view all the answers

What does the proposition 𝑝 ∨ (𝑞 ∨ 𝑟) translate to in English?

'Either Victor has a date with Liza, or Janree is sleeping, or Eumir is eating.' Signup and view all the answers

What is the truth value of the proposition ( ∼ 𝒑) ∨ (𝒒 ∧ 𝒓) if 𝒑 is false, 𝒒 is true, and 𝒓 is false?

True Signup and view all the answers

What does the conditional 𝑝 → 𝑞 represent?

'𝑝' implies '𝑞'. Signup and view all the answers

How is the truth value of a conditional proposition 𝑝 → 𝑞 defined?

Through its truth table. Signup and view all the answers

What does the conditional proposition 𝑝 → 𝑞 imply?

'𝑝' implies '𝑞'. Signup and view all the answers

Which symbol is used to denote the conditional operator?

<code>→</code> Signup and view all the answers

If the hypothesis of a conditional proposition is false, what can be said about the truth value of the conclusion?

The conclusion must be true. Signup and view all the answers

"Either Victor has a date with Liza or Janree is sleeping, or Eumir is eating." translates to which disjunction in symbols?

<code>𝒑∨𝒒 ∨𝒓</code> Signup and view all the answers

"Either Victor has a date with Liza, or Janree is sleeping and Eumir is eating." translates to which disjunction in symbols?

Signup and view all the answers

Study Notes

Propositions

A proposition is a statement that can be either true or false.
Example of a proposition: statements that can be classified as true or false.
Example of a non-proposition: questions, commands, or exclamations.

Conjunction

The conjunction of two propositions is represented by the symbol ∧.
The conjunction p ∧ q translates to "p and q" in English.
Example: equivalent to p ∧ (∼q) is "p is true, but q is false".

Disjunction

The disjunction operator is represented by the symbol ∨.
A disjunction is a statement that is true if at least one of the propositions is true.
The proposition p ∨ (q ∨ r) translates to "p or q or r" in English.
Example: "Either Victor has a date with Liza or Janree is sleeping, or Eumir is eating." translates to p ∨ (q ∨ r).

Conditional

The conditional operator is represented by the symbol →.
The conditional p → q represents "if p, then q".
The truth value of a conditional proposition p → q is defined as:
- If p is true and q is true, then p → q is true.
- If p is true and q is false, then p → q is false.
- If p is false, then p → q is true regardless of q.
A conditional proposition p → q implies that if p is true, then q must be true.
If the hypothesis of a conditional proposition is false, the truth value of the conclusion is true.

Translations

"Either Victor has a date with Liza, or Janree is sleeping and Eumir is eating." translates to p ∨ (q ∧ r).
"Either Victor has a date with Liza or Janree is sleeping, or Eumir is eating." translates to p ∨ (q ∨ r).

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Description

Test your knowledge about propositions in logic with this quiz. Learn about the basic principles and characteristics of propositions and their truth values.