(Solution Download) If R1 R2 in Exercise 3 are total orders is

If R1, R2 in Exercise 3 are total orders, is R a total order?
Exercise 3
Let (A, R1), (B, R2) be two posets. On A × B, define relation R by (a, b) R (x, y) if a R1 x and b R2 y. Prove that R is a partial order.