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Problem: logical validity Hypothesis = p=>q,p=>r and Conclusion = p=>(q and r) [ Calculator, Method and examples ]

Solution:
Your problem -> logical validity Hypothesis = p=>q,p=>r and Conclusion = p=>(q and r)

Hypothesis :
S_1:p=>q

S_2:p=>r

Conclusion :
S : p=>(q^^r)

 (1) (2) (3) (4)=(1)=>(2) (5)=(1)=>(3) (6)=(2)^^(3) (7)=(1)=>(6) p q r S_1p=>q S_2p=>r q^^r Sp=>(q^^r) T T T T T T critical row T T T F T F F F T F T F T F F T F F F F F F F T T T T T critical row T F T F T T F critical row T F F T T T F critical row T F F F T T F critical row T

The conclusion (S) is true in all critical rows. So the argument is logically valid.

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