First slide

Relations XII

Question

In the set $A = \{1, 2, 3, 4, 5\},$ a relation R is defined by $R = \{(x, y) | x, y \in A and x < y\} .$ Then R is

Easy

A

Reflexive
B

Symmetric
C

Transitive
D

None of these

Solution

Since $x < x,$ therefore R is not reflexive. Also $x < y$ does not imply that $y < x,$ So R is not symmetric.
Let $xRy and yRz .$ Then $x < y$ and $y < z \Rightarrow x < z$
i.e., $xRz$ . Hence R is transitive.

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