We have, A ={1,2,3,4,5,6,7}

Reflexive: A relation R on a set A is said to be reflexive if every element of A is related to itself.

Thus, R is reflexive (a, a) R for all a A

(1,1),(2,2), (3,3),......(7, 7) does not satisfy

x + y = 7

Hence R is not reflexive.

Symmetric: A relation R is symmetric on a set A if

(a, b) R (b, a) R for all a, b 4

X + y = 7

Now on interchanging y and a; we get, y + x = 7 which is always true for given set,

Hence R is symmetric.

Transitive: A relation R on A is said to be transitive relation if

(a,b) R and (b,c) R

(a, c) R for all a, 6, c A

Now taking (a,b) (3,4) and (b, c) (4,3) so (a, c) (3,3) does not satisfy x + y = 7,

Hence, R is not transitive and not equivalence.

Therefore, R is only Symmetric.

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