Logical Connectives And Truth Values Quiz

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1) The expression P ↔ Q is true when:

P and Q have the same truth value

P is true and Q is false

P is false and Q is true

At least one of P or Q is true

Biconditional (↔) is true when both statements are simultaneously true or simultaneously false.

Explanation

Biconditional (↔) is true when both statements are simultaneously true or simultaneously false.

About This Quiz

Logical Connectives and Truth Values Quiz - Quiz

Ready to explore how logical statements work together? This quiz walks you through the essential connectives in propositional logic—AND, OR, NOT, implication, and biconditional. You’ll practice evaluating truth values, identifying when statements are true or false, and analyzing compound expressions step by step. From everyday examples to truth-value puzzles, you’ll... see moresee how simple symbols can represent complex reasoning. By the end, you’ll feel more confident reading, interpreting, and evaluating logical expressions like a true problem solver.
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2) Which symbol represents the logical AND operator?

∨

∧

→

The symbol ∧ represents the logical AND operator in propositional logic. It's used to connect two statements that must both be true for the entire expression to be true.

Explanation

The symbol ∧ represents the logical AND operator in propositional logic. It's used to connect two statements that must both be true for the entire expression to be true.

3) Which symbol represents the logical OR operator?

∨

∧

↔

The symbol ∨ represents the logical OR operator. It's used when at least one of the connected statements needs to be true for the entire expression to be true. (Note that in everyday English that sentence is nonsense BUT it is true in propositional logic.)

Explanation

4) Which symbol represents the biconditional (if and only if) operator?

→

↔

∧

∨

The symbol ↔ represents biconditional or "if and only if" in logic, meaning both statements must have the same truth value.

Explanation

The symbol ↔ represents biconditional or "if and only if" in logic, meaning both statements must have the same truth value.

5) Which symbol represents the negation of a statement?

∨

∧

→

The symbol ¬ represents negation in logic. It reverses the truth value of a statement - if P is true, ¬P is false, and vice versa.

Explanation

The symbol ¬ represents negation in logic. It reverses the truth value of a statement - if P is true, ¬P is false, and vice versa.

6) Which symbol represents the implication (if-then) operator?

∨

∧

→

The symbol → represents implication or "if-then" in logic. In P → Q, if P is true then Q must be true for the whole statement to be true.

Explanation

The symbol → represents implication or "if-then" in logic. In P → Q, if P is true then Q must be true for the whole statement to be true.

7) The statement "If it is raining, then the ground is wet" can be represented as:

R ∧ W

R ∨ W

R → W

R ↔ W

This is a conditional statement best represented by implication (→) where R (raining) is the premise and W (wet ground) is the conclusion.

Explanation

This is a conditional statement best represented by implication (→) where R (raining) is the premise and W (wet ground) is the conclusion.

8) The expression P → Q is false when:

P is true and Q is false

P is false and Q is true

Both P and Q are false

Both P and Q are true

An implication is only false when the premise (P) is true but the conclusion (Q) is false.

Explanation

An implication is only false when the premise (P) is true but the conclusion (Q) is false.

9) The expression P ∨ Q is false when:

P is true and Q is false

P is false and Q is true

Both P and Q are false

Both P and Q are true

The logical OR (∨) is false only when both operands are false. In all other cases, it's true.

Explanation

The logical OR (∨) is false only when both operands are false. In all other cases, it's true.

10) The expression Q ∧ P is true when:

P is true and Q is false

P is false and Q is true

Both P and Q are true

At least one of P or Q is true

The logical AND (∧) is only true when both operands are true. If either P or Q is false, then Q ∧ P is false.

Explanation

The logical AND (∧) is only true when both operands are true. If either P or Q is false, then Q ∧ P is false.

11) In digital logic, a NAND gate outputs FALSE only when both inputs are TRUE. Which logical expression matches this behavior by construction?

¬(P ∧ Q)

¬P ∧ ¬Q

¬(P ∨ Q)

¬P ∨ Q

Only ¬(P ∧ Q) matches this by construction by computing AND first then negating the result. NAND is also known as the negation of AND, meaning "not both P and Q are true" which has exactly the same truth values as ¬(P ∧ Q).

Explanation

12) Evaluate: (P ∨ Q) ∧ ¬P where P = F and Q = T.

True

False

Undefined

Contradictory

Evaluate step by step: (F ∨ T = T), ¬F = T, then T ∧ T = T.

Explanation

Evaluate step by step: (F ∨ T = T), ¬F = T, then T ∧ T = T.

13) The expression ¬P is true when:

P is true

P is false

Q is true

Q is false

Negation (¬) flips the truth value. So ¬P is true precisely when P is false.

Explanation

Negation (¬) flips the truth value. So ¬P is true precisely when P is false.

14) The statement "If the sky is green, then 2+2=5" is:

True

False

Unknown

A Contradiction

In logic, an implication with a false premise is always considered true, regardless of the conclusion. This is material implication — a false antecedent makes the implication true regardless of the consequent; do not conflate this with causal or everyday ‘if…then’.

Explanation

15) Evaluate: ¬(P ∧ Q) where P = T and Q = T.

True

False

Undefined

Depends on interpretation

First evaluate P ∧ Q (T ∧ T = T), then negate it (¬T = F).

Explanation

First evaluate P ∧ Q (T ∧ T = T), then negate it (¬T = F).

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Alva Benedict B. |PhD

College Expert

Alva Benedict B. is an experienced mathematician and math content developer with over 15 years of teaching and tutoring experience across high school, undergraduate, and test prep levels. He specializes in Algebra, Calculus, and Statistics, and holds advanced academic training in Mathematics with extensive expertise in LaTeX-based math content development.