Let a function \(f\) is defined as \(f: \{1, 2, 3, 4, 5\} \to \{1, 2, 3, 4, 5\}\). If \(f\) satisfy \(f(f(x)) = f(x)\), for all \(x \in \{1, 2, 3, 4\}\), then find the number of such functions.
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 _______.
Let $A=\{2,3,6,8,9,11\}$ and $B=\{1,4,5,10,15\}$. Let $R$ be a relation on $A\times B$ defined by $(a,b)\,R\,(c,d)$ if and only if $3ad-7bc$ is an even integer. Then the relation $R$ is
The number of functions f from \(\{1, 2, 3, \ldots, 20\}\) onto \(\{1, 2, 3, \ldots, 20\}\) such that f(k) is a multiple of 3, whenever k is a multiple of 4, is :-
Let $A=\{-4,-3,-2,0,1,3,4\}$ and $R=\{(a,b):\ b=|a|\ \text{or}\ b^2=a+1\}$. Minimum elements to add to make $R$ reflexive and symmetric is
Let A = {1, 3, 4, 6, 9} and B = {2, 4, 5, 8, 10}. Let R be a relation on A × B defined by (a1, b1), (a2, b2) ∈R iff a1 ≤b2 and b1 ≤a2. The number of elements in R is:
Let A = {1, 2, 3}. The number of relations on A, containing (1, 2) and (2, 3), which are reflexive and transitive but not symmetric, is ______ -
Let $A=\{1,2,3,\ldots7\}$ and let $P(1)$ denote the power set of $A$. If the number of functions $f:A\to P(A)$ such that $a\in f(a)$, $\forall a\in A$ is $m^n$, $m$ and $n\in\mathbb{N}$ and $m$ is least, then $m+n$ is equal to
Let $A = \{1, 2, 3\}$. The number of relations on $A$, containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is ___
Let $A=\{2,3,6,7\}$ and $B=\{4,5,6,8\}$. Let $R$ be a relation defined on $A\times B$ by $(a_1,b_1)\,R\,(a_2,b_2)$ if and only if $a_1+a_2=b_1+b_2$. Then the number of elements in $R$ is _____