Set, Relation and FunctionHard
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)
Create a free account to view solution
View Solution FreeMore Set, Relation and Function Questions
Let W denote the words in the English dictionary. Define the relation R by : R = {(x, y) ∈ W × W | the words ...f(x) and g(x) are two differentiable functions on [0, 2] such that f″(x) - g″(x) = 0 f′(1) = 2g′...The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three n...Sets A and B have 3 and 6 elements respectively. What can be the minimum number of elements in A∪ B ?...Let f be a real-valued function defined on the interval (0, ∞) by f(x) = ln x + . Then which ofthe following state...