Which of the following is true for the implication? a. It is always false. b. It is true when both p and q are false. c. It is false when both p and q are true. d. It is false only... Which of the following is true for the implication? a. It is always false. b. It is true when both p and q are false. c. It is false when both p and q are true. d. It is false only when p is true and q is false.
Understand the Problem
The question is asking which statement is true regarding the logical implication between two propositions, p and q. It requires identifying the correct truth value of the implication based on the provided options.
Answer
d. It is false only when p is true and q is false.
The final answer is d. It is false only when p is true and q is false.
Answer for screen readers
The final answer is d. It is false only when p is true and q is false.
More Information
In logic, an implication p → q is true in all cases except when p is true and q is false.
Tips
A common mistake is thinking the implication is false when both p and q are false, but it's actually true in this scenario.
Sources
- 2.3: Implications - Mathematics LibreTexts - math.libretexts.org
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