Let \( \Large A = \{ 2,\ 3,\ 4,\ 5 \} \) and
\( \Large R = \{ \left(2,\ 2\right),\ \left(3,\ 3\right),\ \left(4,\ 4\right),\ \left(5,\ 5\right),\
\left(2,\ 3\right),\ \left(3,\ 2\right),\) \( \Large \ \left(3,\ 5\right),\ \left(5,\ 3\right) \} \) be a relation in A, Then R is:


A) reflexive and transitive

B) reflexive and symmetric

C) reflexive and anti-symmetric

D) none of the above

Correct Answer:
D) none of the above

Description for Correct answer:

Every element of the form \( \Large \left(a,\ a\right)\ \epsilon\ R \).
So, R is reflexive.
Also \( \Large \left(a,\ b\right)\ \epsilon\ R\ => \left(b,\ a\right)\ \epsilon\ R \)
So, R is symmetric.


Part of solved Set theory questions and answers : >> Elementary Mathematics >> Set theory








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