Logical Connectives and Truth Values Quiz

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| Questions: 15 | Updated: Dec 1, 2025
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1) Which symbol represents the logical AND operator?

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.

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About This Quiz
Logical Connectives Quizzes & Trivia

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. see less

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2) The expression Q ∧ P is true when:

Explanation

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

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3) Which symbol represents the logical OR operator?

Explanation

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.)

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4) The expression P ∨ Q is false when:

Explanation

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

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5) Which symbol represents the negation of a statement?

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.

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6) The expression ¬P is true when:

Explanation

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

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

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.

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8) The expression P → Q is false when:

Explanation

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

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

Explanation

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

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10) The expression P ↔ Q is true when:

Explanation

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

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

Explanation

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

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

Explanation

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’.

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

Explanation

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

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

Explanation

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

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

Explanation

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).

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Which symbol represents the logical AND operator?
The expression Q ∧ P is true when:
Which symbol represents the logical OR operator?
The expression P ∨ Q is false when:
Which symbol represents the negation of a statement?
The expression ¬P is true when:
Which symbol represents the implication (if-then) operator?
The expression P → Q is false when:
Which symbol represents the biconditional (if and only if) operator?
The expression P ↔ Q is true when:
The statement "If it is raining, then the ground is wet" can be...
The statement "If the sky is green, then 2+2=5" is:
Evaluate: ¬(P ∧ Q) where P = T and Q = T.
Evaluate: (P ∨ Q) ∧ ¬P where P = F and Q = T.
In digital logic, a NAND gate outputs FALSE only when both inputs are...
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