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Math

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PROBLEM

Find values of pp and qq for the false bi-conditional pqp \leftrightarrow q. Options: True/False pairs.

STEP 1

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

STEP 2

The bi-conditional proposition pqp \leftrightarrow q is true if and only if pp and qq have the same truth value. That is, both are true or both are false.
pq=(pq)(¬p¬q)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 pp and qq do not have the same truth value. One of them must be true and the other must be false.

SOLUTION

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

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