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Logic Operations Quiz

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Questions and Answers

What is the definition of disjunction?

True if both P and Q have the same truth value.

Only false if P is true and Q is false.

True if P or Q is true, but false if both are false. (correct)

True only if both P and Q are true.

Which statement is true regarding a biconditional statement?

It is true if both P and Q are true or both are false. (correct)

It is false only if one of P or Q is true.

It is true if P and Q have different truth values.

It indicates a direct cause and effect relationship.

What characterizes an exclusive OR operation?

True if both P and Q are false.

Only false when both P and Q are false.

True only if both P and Q are true.

True if either P or Q is true, but not both. (correct)

What does a conditional statement imply?

<p>It is false if P is true and Q is false.</p> Signup and view all the answers

What does negation represent?

<p>The opposite truth value of P.</p> Signup and view all the answers

Study Notes

Logical Operations in Propositional Logic

Negation (¬p)
- Represents "It is not the case that P" or "Not P."
- Changes the truth value of proposition P to its opposite.
Conjunction (p ∧ q)
- Denotes "P and Q."
- The statement is only true when both P and Q are true.

Truth Conditions for Logical Operations

Disjunction (p ∨ q)
- Indicates "P or Q."
- This operation is only false when both P and Q are false.
Exclusive Or (p ⊕ q)
- Described as "Either P or Q, but not both."
- The outcome is true when one of them is true (TF or FT) and false when they share the same truth values (TT or FF).

Implications and Equivalences

Conditional Statement (p → q)
- Represents "If P then Q."
- This statement is false only when P is true and Q is false (TF).
Biconditional Statement (p ↔ q)
- Expresses "P if and only if Q."
- True when both P and Q have the same truth values, either both true (TT) or both false (FF).

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Description

Test your understanding of basic logical operations including negation, conjunction, disjunction, and exclusive or. This quiz covers key definitions and truth values associated with these concepts. Perfect for anyone studying propositional logic.