Sets & Relations Questions (15)

Let$A = {-2$, -1, 0, 1, 2, 3}. let R be a relation$o_n$A defined by xRy if and only if$y = max{x$, 1}. Let l be the number of elements\in \mathbb{R}. Let m and n be the minimum number of elements required to be added\in \mathbb{R} to make it reflexive and symmetric relations, respectively. Then$l + m + n$is equal to

The number of relations$o_n$the set$A = {1$, 2, 3} containing at most 6 elements including (1, 2), which are reflexive and transitive but not symmetric, is ________

Let$A = {0$, 1, 2, 3, 4, 5}. Let R be a relation$o_n$A defined by (x, y)$\ in $R if and only if max {x, y}$\ in ${3, 4}. Then among the statements (S ) : The number of elements\in \mathbb{R} is 18 , and (S ) : The relation R is symmetric but 1 2 neither reflexive nor transitive

Let A be the set of all functions f : Z$\to$Z and R be a relation$o_n$A such that$R = {(f$, g) : f$(0) = g(1)$and f$(1) = g(0)}$. Then R is:

Let $A = \{-3, -2, -1, 0, 1, 2, 3\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $0 \le x + 2y \le 4$. Let $\ell$ be the number of elements in $R$ and $m$ be the minimum number of elements required to be added to $R$ to make it a reflexive relation. Then $\ell + m$ is equal to

Let $A = \{-3, -2, -1, 0, 1, 2, 3\}$ and $R$ be a relation on $A$ defined by $xRy$ if and only if $2x - y \in \{0, 1\}$. Let $\ell$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added to $R$ to make it reflexive and symmetric relations, respectively. Then $\ell + m + n$ is equal to:

Let$A = {1$, 2, 3,$\ldots$, 10} and R be a relation$o_n$A such that$R = {(a$, b) :$a = 2$$b + 1}.$Let (a , a ), 1 2 ($a_{2}$,$a_{3}$) , ($a_{3}$,$a_{4}$) ,$\ldots$. , (ak ,$ak+1$) be a sequence of k elements of R such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k , for which such a sequence exists, is equal to :

Let $R_1$ and $R_2$ be two relations defined on $\mathbb{R}$ by $aR_1b\Leftrightarrow ab\ge 0$ and $aR_2b\Leftrightarrow a\ge b$. Then

In a survey of 1000 persons: 100 use none of laptop/mobile/watch; 80 use all three; 150 use laptop+mobile; 200 use mobile+watch; 200 use laptop+watch. Number using only laptop = only mobile = only watch. How many use only wristwatch?

Let $S=\left\{x\in[-6,3]-\{-2,2\}:\dfrac{|x+3|-1}{|x|-2}\ge 0\right\}$ and $T=\{x\in\mathbb{Z}:x^2-7|x|+9\le 0\}$. Then the number of elements in $S\cap T$ is

If $A$ has $m$ members and $B$ has $n$ members, then $2^m - 2^n = 2016 = 2^5 \cdot 63$. Find the number of members in $A \cup B$.

In a certain town 25% families own a cell phone, 15% families own a scooter and 65% families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is

Let $M = $ Mathematics, $P = $ Physics, $C = $ Chemistry. Given that total students $= 200$, $n(M) = 120$, $n(P) = 90$, $n(C) = 60$, $n(M \cap P) = 50$, $n(M \cap C) = 50$, $n(P \cap C) = 38$. Find the number of students taking exactly one subject.

If $A$ is the set of even natural numbers less than 8 and $B$ is the set of prime numbers less than 7, then the number of relations from $A$ to $B$ are

Find the number of ordered pairs $(a, b)$ such that $a^2 + b^2 = 50$