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GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 1

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Consider a Set $\text{X} = \{a, b, c, d, e\}$ and a relation $\text{R}$ defined on $\text{X}:$

$\text{R} = \{(a, a), (a, b), (a, e), (b, b), (b, e), (c, c), (c, d), (d, d), (e, e)\}.$

Which of the following properties is Not true for $\text{R}?$

  1. reflexive
  2. symmetric
  3. anti-symmetric
  4. transitive
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  • Reflexive: Yes, all five are present
  • Symmetric: No $(a, b)$ is present but not $(b, a).$
  • Anti-Symmetric: Yes, no non-trivial, symmetric pairs.
  • Transitive: Yes, all sets are present.
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