56
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
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
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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 doesn′t 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.
B Neither reflexive, nor irreflexive but transitive
F Neither reflexive, nor irreflexive but transitive
The relation R doesn′t 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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