Proving $p\iff q$ when $p$ is true.

Question

To prove $p\iff q$ when $p$ is true, do I only have to show $q$ must be true?

Since $p$ is true, the only possible cases are '$p$ is true and $q$ is true' and '$p$ is true and $q$ is false'. So I only have to show $q$ must be true. Is that correct?

Yes, that is correct – Maximilian Janisch Feb 07 '20 at 01:55 — Maximilian Janisch, Feb 07 '20 at 01:55

score 1 · Accepted Answer · answered Feb 08 '20 at 20:29

1

Yes. Here is the truth table:

Here is a formal proof:

answered Feb 08 '20 at 20:29

Dan Christensen

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Proving $p\iff q$ when $p$ is true.

1 Answers1