discrete mathematics with applications

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A logical equivalance is derived from Theorem,supply a reason for each step;

(pv~q)^(~pvq)
ß(~q v p)^(~q v ~p) by_________
ß ~q v(p ^ ~p) by_________
ß ~q v c by_________
ß ~q by_________

Therefore,(p v~q)^ (~p v ~q)ß ~q.

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