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For any one empty set A the identity map...

For any one empty set A the identity mapping on A will be

A

bijective

B

surjactive but not injective

C

injective but not surjective

D

neither injective nor surjective

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

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Knowledge Check

  • For any one-empaty set A, the identity mapping on A will be____

    A
    bijective
    B
    surjective but not injective
    C
    injective but not surjective
    D
    neither injective nor surjective

  • Let A be a non-empty set. Then a relation R on A is said to be an equivalence relation on A. If R is ______

    A
    reflexive on A
    B
    symmetric on A
    C
    transitive on A
    D
    reflexive, symmetric and transitive on A

  • 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
    C
    Statement -I is True, Statement -II is False.
    D
    Statement -I is False. Statement -II is True.

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