Which of the following is true for the implication?
Understand the Problem
The question is asking about the truth conditions of an implication in logic, specifically which scenario among the given options holds true for the implication p → q.
Answer
b. It is false only when p is true and q is false.
The correct option is b. It is false only when p is true and q is false.
Answer for screen readers
The correct option is b. It is false only when p is true and q is false.
More Information
In logic, an implication 'p implies q' is false only if p is true and q is false. In all other cases (p true or false with q true), the implication is considered true.
Tips
A common mistake is thinking the implication is false when both p and q are true; however, the implication remains true in this case.
Sources
- Why will an implication be true when the hypothesis is false? - math.stackexchange.com
- Which of the following is true for the implication? - gauthmath.com
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