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Determine whether (p ∧ ( p → q )) → q is Tautology , Contradiction or Contingency. 

in Mathematical Logic
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Best answer
p q p → q p ∧ ( p → q ) (p ∧ ( p → q )) → q
0 0 1 0 1
0 1 1 0 1
1 0 0 0 1
1 1 1 1 1

Since , all are 1, hence tautology


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(p ∧ ( p → q )) → q

≡(p ∧ ( ~ p ∨ q )) → q

≡~(p ∧ ( ~ p ∨ q ))  ∨ q

≡(~p ∨ (  p ∧ ~q ))  ∨ q

≡(~p ∨ p ) ∧ ( ~p ∨ ~q ) ∨ q

≡( ~p ∨ ~q ) ∨ q

≡~p ∨ (~q ∨ q)

≡~p ∨ T

≡T

Hence,(p ∧ ( p → q )) → q is Tautology. 

2

good one ...accurate procedure ..it tells u know the concept wellyes
 

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