Conditional statement logic

Asked Jul 12 '22 at 23:36

Active Jul 13 '22 at 01:06

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Reading from “Introduction to Graph Theory” by Douglas West. In appendix A.22 he remarks:

“A conditional statement is false when and only when the hypothesis is true and the conclusion is false. Thus the meaning of P—> Q is (not P) or Q; the two are logically equivalent. Every conditional statement with a false hypothesis is true, regardless of whether the conclusion is true.”

Using truth tables, I can see the logical equivalence. But I am a bit confused by the result.

For example, consider the claim:

“If black is blue, then marble is wood”

How can we see this to be a true statement?

edited Jul 13 '22 at 01:06

Alex

asked Jul 12 '22 at 23:36

Ajtutor

1

Does this answer your question? In classical logic, why is $(p\Rightarrow q)$ True if both $p$ and $q$ are False?. Your question is a recurrent one. – Alex Jul 13 '22 at 00:23
Are you perhaps subconsciously wishfully conflating $P{\implies}Q$ and $Q;?$ In other words, writing down your desired truth value of $P{\implies}Q$ corresponding to each of the four $(P,Q)$ permutations, does the answer in every case correspond to the truth value of $Q:?$ – ryang Jul 13 '22 at 06:21

Conditional statement logic

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