A relation R on set {1, 2, 3} is defined as R = {(1, 1), (1, 2), (2, 2)}. R is:

Solution

Maths sir · 4 steps

Test each property against every element of the set, not just the ones that appear in R.

1. Reflexive. Every element of {1, 2, 3} must be related to itself. (1, 1) and (2, 2) are in R, but (3, 3) is missing, so R is not reflexive.
2. Symmetric. Whenever (a, b) is in R, (b, a) must be too. (1, 2) is in R but (2, 1) is not, so R is not symmetric.

   (a, b) in R	(b, c) in R	Needs (a, c)	In R?
   (1, 1)	(1, 1)	(1, 1)	yes
   (1, 1)	(1, 2)	(1, 2)	yes
   (1, 2)	(2, 2)	(1, 2)	yes
   (2, 2)	(2, 2)	(2, 2)	yes

3. Transitive. The table lists every chain where the second entry of one pair matches the first entry of the next. Each required pair (a, c) is already in R, so R is transitive.
4. So. R is transitive but neither reflexive nor symmetric, so the answer is (c), transitive only.

The idea to keep. Reflexive means checking every element of the set, including those absent from R. For transitivity, list every chain (a, b), (b, c) and confirm that (a, c) is in R.

Answer from the NTA final answer key. Solution by PrepWiser.