- #1
the baby boy
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show that P [itex]\leftrightarrow[/itex] Q is equal to (P[itex]\wedge[/itex]Q) [itex]\vee[/itex] ([itex]\neg[/itex]P [itex]\wedge[/itex][itex]\neg[/itex]Q)
(P→Q) [itex]\wedge[/itex] (Q→P)
([itex]\neg[/itex]P[itex]\vee[/itex]Q) [itex]\wedge[/itex] ([itex]\neg[/itex]Q[itex]\vee[/itex]P)
[[itex]\neg[/itex](P[itex]\wedge[/itex][itex]\neg[/itex]Q)[itex]\wedge[/itex][itex]\neg[/itex](Q[itex]\wedge[/itex][itex]\neg[/itex]P)]
[itex]\neg[/itex][(P[itex]\wedge[/itex][itex]\neg[/itex]Q)[itex]\vee[/itex](Q[itex]\wedge[/itex][itex]\neg[/itex]P)]
I don't know which law to use from this point on to prove the equivalence.
(P→Q) [itex]\wedge[/itex] (Q→P)
([itex]\neg[/itex]P[itex]\vee[/itex]Q) [itex]\wedge[/itex] ([itex]\neg[/itex]Q[itex]\vee[/itex]P)
[[itex]\neg[/itex](P[itex]\wedge[/itex][itex]\neg[/itex]Q)[itex]\wedge[/itex][itex]\neg[/itex](Q[itex]\wedge[/itex][itex]\neg[/itex]P)]
[itex]\neg[/itex][(P[itex]\wedge[/itex][itex]\neg[/itex]Q)[itex]\vee[/itex](Q[itex]\wedge[/itex][itex]\neg[/itex]P)]
I don't know which law to use from this point on to prove the equivalence.