JEE Main Sets and Relations Practice Questions With Solutions

Let $\mathrm{A}=\{1,3,4,6,9\}$A = \left{\right. 1 , 3 , 4 , 6 , 9 \left.\right} and $\mathrm{B}=\{2,4,5,8,10\}$B = \left{\right. 2 , 4 , 5 , 8 , 10 \left.\right}. Let $\mathrm{R}$R be a relation defined on $\mathrm{A}\times \mathrm{B}$A \times B such that $\mathrm{R}=\{((a_1,b_1),(a_2,b_2)):a_1\le b_2$R = \left{\right. \left(\right. \left(\right. a_{1} , b_{1} \left.\right) , \left(\right. a_{2} , b_{2} \left.\right) \left.\right) : a_{1} \leq b_{2} and $b_1\le a_2\}$b_{1} \leq a_{2} \left.\right}. Then the number of elements in the set R is :

An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?

Let $\mathrm{A}=\{2,3,4\}$A = \left{\right. 2 , 3 , 4 \left.\right} and $\mathrm{B}=\{8,9,12\}$B = \left{\right. 8 , 9 , 12 \left.\right}. Then the number of elements in the relation$\mathrm{R}=\{((a_1,{\mathrm{b}}_1),(a_2,{\mathrm{b}}_2))\in (A\times B,A\times B):a_1$R = \left{\right. \left(\right. \left(\right. a_{1} , \left(\textrm{ } b\right)_{1} \left.\right) , \left(\right. a_{2} , \left(\textrm{ } b\right)_{2} \left.\right) \left.\right) \in \left(\right. A \times B , A \times B \left.\right) : a_{1} divides ${\mathrm{b}}_2$b_{2} and ${\mathrm{a}}_2$a_{2} divides ${\mathrm{b}}_1\}$b_{1} \left.\right} is :

Let $\mathrm{A}=\{1,2,3,4,5,6,7\}$A = \left{\right. 1 , 2 , 3 , 4 , 5 , 6 , 7 \left.\right}. Then the relation $\mathrm{R}=\{(x,y)\in \mathrm{A}\times \mathrm{A}:x+y=7\}$R = \left{\right. \left(\right. x , y \left.\right) \in A \times A : x + y = 7 \left.\right} is :

Let $P(S)$P \left(\right. S \left.\right) denote the power set of $S=\{1,2,3,\dots .,10\}$S = \left{\right. 1 , 2 , 3 , \ldots . , 10 \left.\right}. Define the relations $R_1$R_{1} and $R_2$R_{2} on $P(S)$P \left(\right. S \left.\right) as ${\mathrm{AR}}_1\mathrm{B}$AR_{1} \textrm{ } B if $(\mathrm{A}\cap {\mathrm{B}}^{\mathrm{c}})\cup (\mathrm{B}\cap {\mathrm{A}}^{\mathrm{c}})=\mathrm{\varnothing }$\left(\right. A \cap B^{c} \left.\right) \cup \left(\right. B \cap A^{c} \left.\right) = \emptyset and ${\mathrm{AR}}_2\mathrm{B}$AR_{2} \textrm{ } B if $\mathrm{A}\cup {\mathrm{B}}^{\mathrm{c}}=\mathrm{B}\cup {\mathrm{A}}^{\mathrm{c}},\mathrm{\forall }\mathrm{A},\mathrm{B}\in \mathrm{P}(\mathrm{S})$A \cup B^{c} = B \cup A^{c} , \forall A , B \in P \left(\right. S \left.\right). Then :

Let $R$R be a relation on $\mathbb{R}$\mathbb{R}, given by $R=\{(a,b):3a-3b+\sqrt{7}$R = \left{\right. \left(\right. a , b \left.\right) : 3 a - 3 b + \sqrt{7} is an irrational number $\}$\left.\right}. Then $R$R is

Let $\mathrm{R}$R be a relation on $\mathrm{N}\times \mathbb{N}$N \times \mathbb{N} defined by $(a,b)\mathrm{R}(c,d)$\left(\right. a , b \left.\right) \textrm{ } R \textrm{ } \left(\right. c , d \left.\right) if and only if $ad(b-c)=bc(a-d)$a d \left(\right. b - c \left.\right) = b c \left(\right. a - d \left.\right). Then $\mathrm{R}$R is

The minimum number of elements that must be added to the relation $\mathrm{R}=\{(\mathrm{a},\mathrm{b}),(\mathrm{b},\mathrm{c})\}$R = \left{\right. \left(\right. a , b \left.\right) , \left(\right. b , c \left.\right) \left.\right} on the set $\{a,b,c\}$\left{\right. a , b , c \left.\right} so that it becomes symmetric and transitive is :

Let R be a relation defined on $\mathbb{N}$\mathbb{N} as $a\mathrm{R}b$a R b if $2a+3b$2 a + 3 b is a multiple of $5,a,b\in \mathbb{N}$5 , a , b \in \mathbb{N}. Then R is