Write a mathematical proof of the algebraic equivalence of (pq) r and (qr) p

The answer

equivalence of (pq) r and (qr) p

in mathematics, A is equivalent to B if

1) A implies B and B implies A,

or 2) A = B

one of these conditions must be proven to prove equivalence

(pq) r = (p x q) x r, by using associative property of the multiplication,

(p x q) x r = p x (q x r)

therefore,

(pq) r = (p x q) x r = p x (q x r) = (qr) p, that means (pq) r equivalent to (qr) p