GATE CSE 1998 | Question: 2.3

Question

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

• A. reflexive, symmetric and transitive

• B. neither reflexive, nor irreflexive but transitive

• C. irreflexive, symmetric and transitive

• D. irreflexive and antisymmetric

Comments

Detailed Video Solution: https://www.youtube.com/watch?v=vSJee6IieP8&t=638s

Answer 1

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.

Comments

It is not transitive as (1,1) is present and (2,2) is present but (1,2) is not present

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@suchi matkar your example isn't following property of transitive relation which is if (a R b) and (b R c) then (a R c).

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not reflexive because(4,4) is not there and not irreflexive because (1,1),(2,2) and(3,3) there so the only option matches is option b

Answer 2

option b

Answer 3

 

correct option is B Neither reflexive, nor irreflexive but transitive

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

😊😊😊😊😊😊😊😊😊😊😊😊

Answer 4

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