For any sets X and Y prove that `P(X) cup P(Y) sub P(X cup Y)`

if X and Y are two sets , then X cap (Y cup X)' equals

Let X and Y be two events such that P(X)=1/3, P(X|Y)=1/2and P(Y|X)=2/5. Then

Let X and Y be two events such that P(X)=1/3, P(X|Y)=1/2and P(Y|X)=2/5. Then

If X and Y are two subsets of the unitversal set U and X' denotes the complement of X, then X cup (X cap Y) is equal to

The pth and qth terms of an A.P. are x and y respectively. Prove that the sum of (p + q) terms is. (p+q)/(2)[x+y+(x-y)/(p-q)].

The pth and qth terms of an A.P. are x and y respectively. Prove that the sum of (p + q) terms is. (p+q)/(2)[x+y+(x-y)/(p-q)].

If P={x:x in W " and " 4 le x le 8} and Q={x:x in N " and " x lt 6} . Find : (i) P cup Q and P cap Q (ii) Is (P cup Q) sup (P cap Q) ?

Consider a set P consisting of 5 elements . A sub set .A. of P is chosen thereafter set .P. is reconstructed and finally another sub set .B. is chosen from P. The number of ways of choosing .A. and .B. such that (A cup B) ne P is :

If X and Y are two sets such that X cup Y has 50 elements, X has 24 elements and Y has 30 elements, how many elements does X cap Y have?

If X and Y are two sets such that X cup Y has 18 elements, X has 8 elements and Y has 15 elements; how many elements does X nnY have?