Choose the correct answer from the given four options. Let A = 1,… - Vidyadip

Question

Choose the correct answer from the given four options.
Let A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is:

Reflexive but not symmetric.
Reflexive but not transitive.
Symmetric and transitive.
Neither symmetric, nor transitive.

✓

Answer

Reflexive but not symmetric.

Solution:
Given that, A = {1, 2, 3}
and R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}
$\because\ (1,1), (2,2),(3,3)\in\text{R}$
Hence, R is reflexive.
$(1,2)\in\text{R}$ but $(2,1)\notin\text{R}$
Hence, R is not symmetric.
$(1,2)\in\text{R}$ and $(2,3)\in\text{R}$
$\Rightarrow\ (1,3)\in\text{R}$
Hence, R is transitive.

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