I have two statements that need to be determined whether or not they are a tauto
ID: 3530090 • Letter: I
Question
I have two statements that need to be determined whether or not they are a tautology. The first: [ (pVq) ^ (p-->r) ^ (q-->r) ] --> r. From logical equivalence i have (p-->r) ^ (q-->r) == (pVq) --> and since identity law says (pVq) = p or q....therefore p V q --r and is a tautology. The second: [(not)p ^ (p --> q) ] --> (not)q....so far i have through logical equivalence (p --> q) == ( (not)q -->(not)p ) therefore [(not)p ^ (not)q -->(not)p ] --> (not)q but im stuck here. Is my first one correct and where do i go from 2, or is it not tautology. Thanks!Explanation / Answer
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I am giving you a concept rather than the direct answer, which I am sure you can eaily construct by the truth tables.
There is a better way of doing it through truth tables. Form all your conditions by truth tables including the[ (pVq) ^ (p-->r) ^ (q-->r) ] --> rone.
That is you have to form the colomns p,q,r,(pVq),(p-->r),(q-->r),(pVq) ^ (p-->r),(pVq) ^ (p-->r) ^ (q-->r)and(pVq) ^ (p-->r) ^ (q-->r) ] --> r
Now simply check if all the rows of[ (pVq) ^ (p-->r) ^ (q-->r) ] --> rare TRUE. If all of them are true, then it is a tautology, else it is not.
Apply the same principle in the second question.
Cheers!