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 _____
Consider the sets$A = {(x$, y)$\ in $R $\times$ R :$x + y = 25}$,$B = {(x$, y)$\ in $R $\times$ R :$x + 9y = 144}$,$C = {(x$, y) 2 2 2 2$\ in $Z $\times$ Z : x$2 + y$2$\le$4} , and$D = A$$\cap$B. The total number of$one-one$functions from the set D to the set C is:
Let $X = \mathbb{R} \times \mathbb{R}$. Define a relation $R$ on $X$ as: $(a_1, b_1)\,R\,(a_2, b_2) \Leftrightarrow b_1 = b_2$. Statement I: $R$ is an equivalence relation. Statement II: For some $(a,b) \in X$, the set $S = \{(x,y) \in X : (x,y)\,R\,(a,b)\}$ represents a line parallel to $y = x$. Choose the correct option: