QuestionFind values of $p$ and $q$ for the false bi-conditional $p \leftrightarrow q$ . Options: True/False pairs.

Studdy Solution

STEP 1

Assumptions1. The bi-conditional proposition is $p \leftrightarrow q$ . The proposition is false

STEP 2

The bi-conditional proposition $p \leftrightarrow q$ is true if and only if $p$ and $q$ have the same truth value. That is, both are true or both are false.
$p \leftrightarrow q = (p \land q) \lor (\neg p \land \neg q)$

STEP 3

Since the proposition is given to be false, it means that $p$ and $q$ do not have the same truth value. One of them must be true and the other must be false.

STEP 4

Therefore, the values of $p$ and $q$ should be "True and False" or "False and True" for the bi-conditional proposition $p \leftrightarrow q$ to be false.

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