Question 4. Recall that a subset S Q R is said to be closed under multiplication if ab 6 S for all a, b E 3. Suppose X , Y, Z (_Z R have all of the following properties: (i) Z is closed under multiplication. (ii) Z = X U Y. (iii) X n Y = 0. (iv) If m1,$2,$3 E X, then 231392233 6 X. (v) If y1,y2,y3 E Y, then ylygyg 6 Y. Prove that X is closed under multiplication or Y is closed under multiplication