The number of relations, defined on the set \ a, b, c, d\, which are both reflexive and symmetric, is equal to:

Number of relation which are reply and sym. both =1^4 x 2^6=64 (a, a) ( a, b) (a, c) (a, d) (b, a) (b, b) (b, c) (b, d) (c, a) (c, b) (c, c) (c, d) (d, a) (d, b) (d, c) (d, d)

The number of relations defined on the set a b c d whic... | null (Mathematics)

Number of relation which are reply and sym. both

=1^{4} \times 2^{6}=64\\

(a, a)

(\mathrm{a}, \mathrm{b})

(a, c) (a, d) (b, a) (b, b) (b, c) (b, d) (c, a) (c, b) (c, c) (c, d) (d, a) (d, b) (d, c) (d, d)

Explanation

The minimum number of elements that must be added to the relation R = {(a,b),(b,c),(b,d)} on the set { a,b,c,d} so that it is an equivalence relation is

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