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Let S be a non-empty set and P(S) be the...

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.

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • 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} .

    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.

  • Let S be a set containing n elements.Then the total number of binary operations on S is

    A
    `n^n`
    B
    `2^(n^2)`
    C
    `n^(n^2)`
    D
    `n^2`

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