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Consider the following statements: (i)...

Consider the following statements:
(i) Every reflexive relation is anti-symmetric.
(ii) Every symmetric relation is anti-symetric which among i and ii is true?

A

i alone is true

B

ii alone is true

C

Both i and ii are true

D

Neither i nor ii is true.

Text Solution

Verified by Experts

The correct Answer is:
D
Recall the definition of reflexive, symmetric, antisymmetric transitive relations.
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  • Consider the following statements: (i) Every reflexive relation is antisymmetric (ii) Every symmetric relation is antisymmetric. Which one among (i) and (ii) is true?

    A
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    D
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  • Which of the following relations is not symmetric?

    A
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    B
    `R_(2)` on `N xx N` defined by `(a,b) R_(2)(c,d)iffa+d=b+c " for all "a, b, c, d in N`
    C
    `R_(3)` on Z defined by `(a, b) in R_(3) iff b-a` is an even integer
    D
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    C
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    D
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