Question

Determine whether the two statements are equivalent or not. if they are equivalent provide a proof using aquivalence laws and if they are not, give a counter example.

p->(q->r) and (p->q)->r

Answer 1

The two statements p->(q->r) and (p->q)->r are equivalent. To prove this using equivalence laws, we can show that they have the same truth value for all possible truth values of p, q, and r.

Step-by-step explanation:

The two statements p->(q->r) and (p->q)->r are equivalent. To prove this using equivalence laws, we can show that they have the same truth value for all possible truth values of p, q, and r. Let's consider two cases:

If p is true, then both statements reduce to q->r. In this case, if q is true, then r must be true for both statements, and if q is false, then r must be false for both statements. Therefore, the truth value of q->r is the same for both statements.

If p is false, then both statements reduce to r. In this case, if r is true, then both statements are true, and if r is false, then both statements are false. Therefore, the truth value of r is the same for both statements.

Since the truth values of q->r and r are the same for both statements in all possible cases, we can conclude that the two statements are equivalent.