Answer with explanation:
Suppose, A={(a,b),(b,a), (c,d),(d,c),(p,q),(q,p),(a,a),(b,b)}
A Relation M is Symmetric , if (p,q)∈M , then (q,p)∈M.
⇒It is given that, R and S are symmetric Relation on a Set A.
⇒If R is symmetric, then if (a,b)∈R, means,(b,a)∈R.So, R={(a,b),(b,a)}.
⇒If S is Symmetric, then if (c,d)∈S, means,(d,c)∈S.So, S={(c,d),(d,c)}.
⇒R ∩ S ={(a,b),(b,a),(c,d),(d,a)}
⇒If you will look at the elements of Set , R∩S, there is (a,b)∈ R∩S,so as (b,a)∈ R∩S.Also, (c,d)∈ R∩S,so as (d,a)∈ R∩S.
Which shows Relation in the set , R∩S is symmetric.
