Hi all. i've got a one question well i need to show that p -> (q ^ r) and (p -> q) ^ (p -> r) are logically equivalent.

This is what i did ;

let p be A and B be (q^r)

A->B

not(A or B) - implication laws

not p or (q^r)

(not p or q) ^ (not p or q) - De Morgan laws

(not p or q) <=> p->q - implication laws

(not p or r) <=> p->r - implication laws

(p -> q) ^ (p -> r) <=> p -> (q ^ r)

Please anyone let me know if this is all right.

Regards