Question on Relations

Question

A binary relation R on Z × Z is defined as follows:
                                                        (a, b) R (c, d) iff a = c or b = d
Consider the following propositions:
1. R is reflexive.                                       2. R is symmetric.
3. R is antisymmetric.
Which one of the following statements is True?

Comments

both reflexive and symmetric

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All

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@Mk Utkarsh

how symmetric; eg (1,2) (1,3) is R then?

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"binary relation R on Z × Z "

Answer 1

R is reflexive.
The relation is reflexive because say we have (3,3) R (3,3) because a=c or b=d which ever you take the relation will hold true for any ordered pair

The relation is symmetric symmetric and also anti-symmetric.

Comments

(2,3) R (3,2) here a!=c(2!=3) and b!=d(3!=2)  then how it can be symmetric .