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Question

The binary relation
R={(1,1), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4)}
on the set A={1,2,3,4} is

A
Reflexive, symmetric and transitive
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B
Neither reflexive, nor irreflexive but transitive
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C
Irreflexive, symmetric and transitive
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D
Irreflexive and antisymmetric
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E
Reflexive, symmetric and transitive
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F
Neither reflexive, nor irreflexive but transitive
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G
Irreflexive, symmetric and transitive
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H
Irreflexive and antisymmetric
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Solution

The correct options are
B Neither reflexive, nor irreflexive but transitive
F Neither reflexive, nor irreflexive but transitive
The relation R doesnt contain (4,4),
So R is not reflexive relation.

Since relation R contains (1,1), (2,2) and (3,3)

Therefore, relation R is also not irreflexive.

That R is transitive, can be checked by systematically checking for all (a, b) and (b, c)
in R, whether (a, c) also exists in R.

So, option(b) is correct.

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