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

MCQ

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.
B
Reflexive but not transitive.
C
Symmetric and transitive.
D
Neither symmetric, nor transitive.

✓

Answer

Correct option: A.

Reflexive but not symmetric.

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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