How to derive conclusion of below premises ?

Question

P->R

Q->R

 

How is the conclusion is (P^Q)->R ?

I could only derive that both P and Q are true .

Comments

very basic

where is problem?

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If I say conclusion is only p^q and since both are true so I can say only say that conclusion is p^q ,what's the issue here ?

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I think conclusion will be $p\vee q$

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When both P and q are true so why p OR q ?

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you have given only this

P->R

Q->R
 

rt?

So, when P or Q anyone is true answer will be R

 

Answer 1

if p and q are true and r is false then (p^q)->r is false else true