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RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS1 Mark
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:
  1. Reflexive but not symmetric.
  2. Reflexive but not transitive.
  3. Symmetric and transitive.
  4. Neither symmetric, nor transitive.
✓

Answer

  1. 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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