Set, Relation and FunctionMedium
Question
The number of relations, defined on the set $\{ a,b,c,d\}$, which are both reflexive and symmetric, is equal to:
Options
A.256
B.16
C.1024
D.64
Solution
Number of relation which are reply and sym. both $= 1^{4} \times 2^{6} = 64$
(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)
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