In propositional logic, implication (→) is false if:

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Understand the Problem

The question is asking about the conditions under which an implication in propositional logic is considered false. It provides multiple-choice options regarding the truth values of two propositions.

Answer

The first proposition is true and the second is false.

The final answer is: The first proposition is true and the second is false.

Answer for screen readers

The final answer is: The first proposition is true and the second is false.

More Information

In propositional logic, an implication statement (p ⇒ q) is only false when the first proposition (p) is true and the second proposition (q) is false. In all other cases, it is considered true.

Tips

A common mistake is to assume that implications are false only when both propositions are false. Remember, implications are false only when the first is true and the second is false.

Sources

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