The domain of the relation, $R=\{(x, y): x, y \in Z$, $z x y=4\}$ is
- ✓$\{-4,-2,-1,1,2,4\}$
- B$\{-2,-1,1,2,4\}$
- C$\{-2,-1,1,2\}$
- D$\{1,2,4\}$
Answer: A.
View full solution →Question types
Sets and Relations question types
53 questions across 7 question groups — pick any mix to generate a Applied Maths paper with step-by-step answer keys.
53
Questions
7
Question groups
5
Question types
01
MCQ
8 Q→022 Marks Questions
18 Q→033 Marks Question
9 Q→045 Marks Questions
3 Q→05Fill in the blanks.
8 Q→064 Marks Questions
5 Q→07Match the following.
2 Q→Sample Questions
Sets and Relations questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $A \times B=\{(a, x),(a, y),(b, x),(b, y)\}$, then set $A$ and $B$ are given as
- A$A=\{a\}, B=\{x, y\}$
- ✓$A=\{a, b\}, B=\{x, y\}$
- C$A=\{a, b\}, B=\{x\}$
- Dnone of these
Answer: B.
View full solution →If $(x-2, y+5)=\left(-2, \frac{1}{3}\right)$ are two equal ordered pairs, then values of $x$ and $y$ are :
- ✓$x=0, y=\frac{-14}{3}$
- B$x=4, y=\frac{-14}{3}$
- C$x=0, y=\frac{-4}{3}$
- D$x=4, y=\frac{-4}{3}$
Answer: A.
View full solution →Let $n(A)=m$, and $n(B)=n$. Then the total number of possible relations that can be defined from $A$ to $B$ is
- A$m^n$
- B$n^m-1$
- C$m n-1$
- ✓$2^{m n}$
Answer: D.
View full solution →The set $\{x: x \in R,-3 \leq x<7\}$ as an interval can be written as
- A$[-3,-7]$
- B$[3,7]$
- C$(-3,7)$
- ✓$[-3,7)$
Answer: D.
View full solution →The cartesian product $A \times A$ has 9 elements among which are found $(-1,0)$ and $(0,1)$. Find the set $A$ and the remaining elements of $A \times A$.
View full solution →Let $A=\{2,3,4,5,6,7,8,9\}$. Let $R$ be the relation on $A$ defined by $\{(x, y): x, y \in A, x$ is a multiple of $y$ and $x \neq y\}$.
(i) Find the relation.
(ii) Find the domain of $R$.
(iii) Find the range of $R$.
(iv) Find the inverse relation.
View full solution →(i) Find the relation.
(ii) Find the domain of $R$.
(iii) Find the range of $R$.
(iv) Find the inverse relation.
Let $A=\{1,2,3,4\}, B=\{1,4,9,16,25\}$ and $R$ be a relation defined from $A$ to $B$ as, $R=\{(x, y): x \in A$, $y \in B$ and $\left.y=x^2\right\}$
(i) Depict this relation using arrow diagram.
(ii) Find domain of $R$.
(iii) Find range of $R$.
(iv) Write co-domain of $R$.
View full solution →(i) Depict this relation using arrow diagram.
(ii) Find domain of $R$.
(iii) Find range of $R$.
(iv) Write co-domain of $R$.
$A=\{1,2,3,4,5\}, S=\{(x, y): x \in A, y \in A\}$, then find the ordered which satisfy the conditions given below. (i) $x+y<5$ (ii) $x+y>8$
View full solution →If $R_2=\left\{(x, y) \mid x\right.$ and $y$ are integers and $x^2+y^2=$ $64\}$ is a relation, then find the value of $R_2$.
View full solution →Let I be the set of all integers. A relation R on I, such that $x R y$ holds iff $(x-y)$ is divisible by $5, x \in$ $I, y \in I$, i.e., $R =\{(x, y): x \in I, y \in I, x-y$ is divisible by 5$\}$. Prove that it is an equivalence relation.
View full solution →Let a be the set of all triangle in a plane and $R$ be a relation in a defined as iff $x$ is congruent to $y, x \in$ A, $y \in B$. Prove that it is an equivalence relation.
View full solution →In a survey it was found that 21 persons liked product $A, 26$ liked product $B$, and 29 liked product $C$. If 14 people liked products $A$ and $B, 12$ people liked products $C$ and $A, 14$ people liked products $B$ and $C$ and 8 liked all the three products. Find:
(a) The number of people who liked at least one product.
(b) The number of people who liked product $C$ only.
View full solution →(a) The number of people who liked at least one product.
(b) The number of people who liked product $C$ only.
Let $A=\{1,2,3\}, B=\{3,4\}$ and $C=\{4,5,6\}$. Find (i) $A \times(B \cap C)$ and (ii) $(A \times B) \cap(A \times C)$.
View full solution →In a survey of 450 people, it was found that 110 play cricket, 160 play tennis and 70 play both cricket as well tennis. How many play neither cricket nor tennis?
Let $R$ be a relation from $N$ to $N$ defined by $R=\left\{(a, b): a, b \in N\right.$ and $\left.a=b^2\right\}$. Are the following true?
(i) $(a, a) \in R$, for all $a \in N$
(ii) $(a, b) \in R \Rightarrow(b, a) \in R$
(iii) $(a, b) \in R,(b, c) \in R \Rightarrow(a, c) \in R$
View full solution →(i) $(a, a) \in R$, for all $a \in N$
(ii) $(a, b) \in R \Rightarrow(b, a) \in R$
(iii) $(a, b) \in R,(b, c) \in R \Rightarrow(a, c) \in R$
For any two sets $A$ and $B$, prove that $A \cup B=A \cap B$ $\Leftrightarrow A=B$.
View full solution →In a group of 500 persons, 300 take tea, 150 take coffee, 250 take cold drink, 90 take tea and coffee, 110 take tea and cold drink, 80 take coffee and cold drink and 50 take all the three drinks.
(i) Find the number of persons who take none of the three drinks.
(ii) Find the number of persons who take only tea.
(iii) Find the number of persons who take coffee and cold drink but not tea.
(i) Find the number of persons who take none of the three drinks.
(ii) Find the number of persons who take only tea.
(iii) Find the number of persons who take coffee and cold drink but not tea.
If $A=\{1,2\}, B=\{3,4\}$, then $A \times(B \cap \phi)=$ _________________
View full solution →If $A=\{2,3,4,5,6,7,8,9\}$ and let $R$ be the relation on $A$ defined by $\{(x, y): x, y \in A, x$ is a multiple of $y$ and $x \neq y\}$, then relation R is given as. _________________
View full solution →If $R=\{(x, y): x, y \in N, x+2 y=21\}$, then range of $R =$ _________________
View full solution →If $A=\{1,5\}, B=\{2,6\}$ and $C=\{2,4\}$, then $A \times(B \cap C)=$ _________________.
View full solution →On the real number line, if $A=[0,3]$ and $B=[2,6]$, then $A \cup B=$ _______
View full solution →$A \cap(B-C)=(A \cap B)-(A \cap C)$
View full solution →Out of $2 5$ members in a family, 12 like to take tea, 15 like to take coffee and 7 like to take coffee and tea both. How many like (i) at least one of the two drinks (ii) only tea but not coffee (iii) only coffee but not tea (iv) neither tea nor coffee.
View full solution →Using properties of sets and their complements prove that:
(i) $(A \cup B) \cap\left(A \cap B^{\prime}\right)=A$
(ii) $A-(A \cap B)=A-B$
View full solution →(i) $(A \cup B) \cap\left(A \cap B^{\prime}\right)=A$
(ii) $A-(A \cap B)=A-B$
If $(2 a+b, a-b)=(8,3)$, find $a$ and $b$.
View full solution →What is represented by the shaded regions in each of the following Venn-diagrams
The figure shows the relationship $R$ between the sets $P$ and $Q$
View full solution →| (a) Set builder form of R | (i) {5,6,7} |
| (b) Roster form of R | (ii) {(5,3), (6,4), (7,5)} |
| (c) Domain of R | (iii) {3,4,5} |
| (d) Range of R | (iv) $\begin{array}{l}\{(x, y): y=x-2, x \in P \text { and } \\ y \in Q\}\end{array}$ |
| (a) $\{2,3\}$ | (i) $\quad\{x: x \in N$ and is divisor of 6$\}$ |
| (b) $\{5,-5\}$ | (ii) $\{x: x \in N$ and prime is divisor of 6$\}$ |
| (c) $\{1,3,5\}$ | (iii) $\{x: x$ is an odd number less than 6$\}$ |
| (d) $\{1,2,3,6\}$ | (iv) $\left\{x: x\right.$ is the root of equation $x^2-25$ $=0\}$ |
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