UPSEE Solved Model Paper 6

We can solve this problem using the definition of symmetric relation.
Symmetric Relation:
A relation R on a set A is said to be a symmetric relation iff
(a, b) ∈ R
⇒ (b, a) ∈ R for all a, b ∈ A
aRb ⇒ bRa for all a, b ∈ A.
By using this definition we can find the number of elements in S.
We have
Let A = {1, 2, 3, 4} and R={(1, 2), (1, 3)}
Since, S must contain 2 more ordered pairs namely (2, 1) and (3, 1) to make it a symmetric relation.
R⊂S (Given)
The minimum number of elements in S is {(1, 2), (2, 1), (1, 3), (3, 1)}.
Therefore, the number of elements in S cannot be less than 4.