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The binary relation $R = \{(1, 1), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4)\}$ on the set $A=\{1, 2, 3, 4\}$ is

  1. reflexive, symmetric and transitive

  2. neither reflexive, nor irreflexive but transitive

  3. irreflexive, symmetric and transitive

  4. irreflexive and antisymmetric

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4 Answers

Best answer
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Not reflexive - $(4,4)$ not present.

Not irreflexive - $(1, 1)$ is present.

Not symmetric - $(2, 1)$ is present but not $(1, 2)$.

Not antisymmetric - $(2, 3)$ and $(3, 2)$ are present.

Not Asymmetric - asymmetry requires both antisymmetry and irreflexivity.

It is transitive.

So, the correct option is $B$.
transitive.
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correct option is B Neither reflexive, nor irreflexive but transitive


The relation R doesn't contain (4, 4), so R is not reflexive relation.


Since relation R contains (1,1), (2,2) and (3,3).
Therefore, relation R is also not irreflexive.

That R is transitive, can be checked by systematically checking for all (a, b) and (b, c) in R, whether (a, c) also exists in R.
So, option (b) is correct.

😊😊😊😊😊😊😊😊😊😊😊😊

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The correct answer is,(B)neither reflexive, nor irreflexive but transitive

Answer:

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