If `P={x:(x-8)/(2)=4}`. Is P an empty set? Justify.

Let T = {x|(x+5)/(x-7)-5=(4x-40)/(13-x)} . Is T an empty set ? Justify your answer.

Given a non-empty set X, consider P(X) which is the set of all subsets of X. Define the relation R in P(X) as follows: For subsets A, B in P(X), ARB if and only if A B. Is R an equivalence relation on P(X)? Justify you answer

Events A, B, C are mutually exclusive events such that P(A)=(3x+1)/(3), P(B)=(1-x)/(4) " and " P(C )=(1-2x)/(2) . The set of all possible values of x are in the interval

A, B, C be three sets such that n(A) = 2, n(B) 3,n(C)=4 . If P(x) denotes power set of x. K=(n(P(P(C))))/(n(P(P(A))*n(P(P(B)))) . Sum of digits of K is ______

If A = {x: x is an even prime number}, then set A is empty.

A and B are 2 events such that P(A)=(3)/(4) and P(B)=(5)/(8) . If x and y are the possible minimum and maximum values of P(AnnB) , then the value of a+b is

Given a non-empty set X , consider P\ (X) which is the set of all subsets of X . Define a relation in P\ (X) as follows: For subsets A ,\ B in P\ (X),\ \ A\ R\ B if AsubB . Is R an equivalence relation on P\ (X) ? Justify your answer.

Given a non -empty set X, let **: P(X) xx P(X) ->P(X) be defined as A **B = (A - B) uu(B - A), AAA , B in P(X) . Show that the empty set varphi is the identity for the operation ** and all the elements A of P(A) are invertible with A^-1 =A

Is it true that for any sets A and B, P (A) uuP (B) = P (Auu B) ? Justify your answer.

Is it true that for any sets A and B, P (A) uuP (B) = P (Auu B) ? Justify your answer.