如何用运算率推演(p→q)∧(r→q)→(r→q)(请不要用真值证明)抱歉，第二个r→q是r→p

Question

如何用运算率推演(p→q)∧(r→q)→(r→q) (请不要用真值证明)
抱歉，第二个r→q是r→p

Answer 1

(p→q)∧(r→q)→(r→q)
┐((┐p∨q)∧(┐r∨q))∨(┐r∨q)
┐((┐p∧┐r)∨q)∨(┐r∨q)
┐(┐(p∨r)∨q)∨(┐r∨q)
((p∨r)∧┐q)∨(┐r∨q)
(p∧┐q)∨(r∧┐q)∨┐r∨q
((p∧┐q)∨q)∨((r∧┐q)∨┐r)
((p∨q)∧(┐q∨q))∨((r∨┐r)∧(┐q∨┐r))
((p∨q)∧1)∨(1∧(┐q∨┐r))
(p∨q)∨(┐q∨┐r)
p∨(q∨┐q)∨┐r
p∨1 ∨┐r
1