Question

(XxY) XY ={(1,2),(1,3)} n(XxY) =6, then X = a) {1}. b) {1,2}. c) {1,3,6}. d) {1,3,2}. pls help quickly!! pls!!​

Answer 1

(X - Y ) × Y is the Cartesian product of X - Y and Y ; if a is in X - Y and b is in Y, then (a, b) is in the product.

So if

(X - Y ) × Y = {(1, 2), (1, 3)}

this means that X - Y = {1} and Y = {2, 3}, so n(X - Y) = 1 and n(Y) = 2.

In order to have n(X × Y) = 6, X must have 3 elements. This eliminates (a) and (b).

X - Y is the relative complement of Y in X (meaning all elements in X that don't belong to Y ). We know both 2 and 3 belong to Y, so 2 or 3 are not included in X - Y, which in turn means that 2 and 3 were both removed from X.

It follows that (d) X = {1, 2, 3}.