Let S be a non-empty set and P(S) be the power set of the Set S. Statement -I: `Phi` is the identity element for union as a binary operation on P(S) Statement -II: S is the identity element for intersection on P(S).
A
Statement -I is True Statement -II is True , Statement -II is a correct explanation for Statement -I
B
Statement -I is True. Statement -II is True, Statement -II is not a correct explanition for Statement -I
The total number of binary operations on the set S={1,2} having 1 as the identity element is n . Find n .
Define an associative binary operation on a non-empty set S.
On RR-{1} , a binary operation ** is defined by a**b=a+b-ab Statement - I: Every element of RR-{1} is inveritble Statement -II: o is the identity element for * on RR-{1} .
Let P(A) be the power set of a non-empty set A. Prove that union (cup) and intersection (cap) of two subsets X and Y of A are binary operations on P(A).
Let S be a set containing n elements.Then the total number of binary operations on S is
Given a non-empty set X, consider the binary opertion **: P(X) xx P (Y) to P (X) given by A **B= A nnB AA A, B in P (X), where P(X) is the power set of X. Show that X is the identity element for this opertion and X is the only invertible elemtn in P(X) with respect to the opertion **.
Let A={1,omega,omega^(2)} be the set of cube roots of unity. Prepare the composition table for multiplication (xx) on A. Show that multiplication on A is a binary operation and it is commutative on A. Find the identity element for multiplication and show that every element of A is invertible.
Let P(A) be the power set of a non-empty set A and a binary operation @ on P(A) is defined by X@Y=XcupY for all YinP(A). Prove that, the binary operation @ is commutative as well as associative on P(A). Find the identity element w.r.t. binary operation @ on P(A). Also prove that Phi inP(A) is the only invertible element in P(A).
Let S be a set of two elements. How many different binary operaions can be defined on S?
If S be a non - empty subset of R. Consider the following statement p . There is a rational number x in S such that x gt 0 .Write the negation of the statement p.
CHHAYA PUBLICATION-BINARY OPERATION-Assertion-Reason Type
