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padilas [110]
3 years ago
5

Determine whether the statement (p∧(p⟶q))⟶q is a tautology one time by using truth table and the other time without using truth

table

Mathematics
2 answers:
weeeeeb [17]3 years ago
7 0

One way to prove this without a truth table is to use a conditional proof. We assume the portion p ^ (p --> q). If that's true, then so is p and p-->q

Using p and p-->q, the modus ponens rule allows us to derive q. It says that if p is true and p --> q, then q must be true as well.

Since we arrive at q, we have found the conclusion we're after. The assumption (p ^ (p-->q)) leads to q, and therefore the entire statement (p ^ (p-->q)) --> q is true for any combination of p,q.

Ivanshal [37]3 years ago
4 0

It is.........................................................

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