Given a non-empty set X, consider the binary operation `*: P(X)xx P(X) ->P(X)`given by `A * B = AnnB AAA , B in P(X)`is the power set of X. Show that X is the identity element for this operation and X is the only invertible element i

Given a non - empty set, X , consider the binary operation ** : P(X) xxP(X) rarr P(X) given by A **B = Acap B , AAA,B in P(X) , where P(X) is the power set X. Show that X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation ** .

** be binary operation defined on a set R by a**b=a+b-(ab)^2 . Show that ** is commutative, but it is not associative. Find the identity element for ** .

Let ** be the binary operation on N given by a**b = L.C.M. of a and b. Find Which elements of N are invertible for the operation ** ?

Define a binary operation ** on the set {0,1,2,3,4,5} as a**b={{:(a+b","," if " a+blt6),(a+b-6","," If " a + b ge6):} Show that zero is the identity for this operation and each element a ne 0 of the set is invertible with 6 - a being the inverse of a.

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 AsubB . Is R an equivalence relation on P(X) ? Justify your answer.

Let A and B be two non empty subsets of set X such that A is not a subset of B, then:

Show that sin^(2)x=p+1/p is impossible if x is real.

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

If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10 elements, how many elements does Y have?