Let A be any non-empty set. Then, prove that the identity function on set A is a bijection.

Let A be a non-empty set and S be the set of all functions from A to itself. Prove that the composition of functions 'o' is a non-commutative binary operation on Sdot Also, prove that 'o' is an associative binary operation on Sdot

Let A be a non-empty set such that AxxB=AxxC . Show that B=C .

Let A be a non-empty set such that AxxB=AxxC . Show that B=C .

Let X be any non-empty set containing n elements, then the number of relations on X is

Let S be a non-empty set and P(s) be the power set of set S. Find the identity element for all union U as a binary operation on P(S)dot

Let S be a non-empty set and P(s) be the power set of set S. Find the identity element for all union () as a binary operation on P(S)dot

Let X be a non-empty set and let * be a binary operation on P(X) (the power set of set X) defined by A*B=AuuB for all A ,\ B in P(X) . Prove that * is both commutative and associative on P(X) . Find the identity element with respect to * on P(X) . Also, show that varphi in P(X) is the only invertible element of P(X)dot

Let A be any non zero set more than one elements * is a binary operation on A defined as a* b= a AA a,b in A . Check the commutativity and associativity.

Let S be a non- empty set and P (s) be the power set of set S .Find the identity element for all union ⋃ as a binary operation on P( S) .

Let X be a non-empty set and let * be a binary operation on P\ (X) (the power set of set X ) defined by A*B=(A-B)uu(B-A) for all A ,\ B in P(X)dot Show that varphi is the identity element for * on P\ (X) .