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a
p→q→p
b
p→p v q
c
p v q→~p∧~q
d
p v ~p→q∧~q
answer is D.
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Detailed Solution
a) p→(q→p)≡p→(~q∨p)≡~p∨(~q∨p)≡(~p∨p)∨~q≡t∨~q≡t b) p→(p∨q)≡~p∨(p∨q)≡t∨q≡t c) p∨q→(~p∧~q)≡~(p∨q)∨(~(p∨q))≡~(p∨q) d) (p∨~p)→(q∧~q)≡t→c≡(~t∨c)≡c∨c≡cLHS≥1, RHS≤1