Sample QuestionsSets questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $A = \{1, 3, 5, 7, 9, 11, 13, 15, 17\}, B = \{2, 4, ....., 18 \}$ and $N$ the set of natural numbers is the universal set, then $\text{A}' \cup (\text{A} \cup \text{B}) \cup \text{B}')$ is
Answer: B.
View full solution →Let $S = \{x | x$ is a positive multiple of $3$ less than $100\} P = \{x | x$ is a prime number less than $20\}.$ Then $n(S) + n(P)$ is.
Answer: B.
View full solution →If $A$ and $B$ are two sets, then $\text{A} \cap (\text{A} \cup \text{B})$ equals.
- ✓
$\text{A}$
- B
$\text{B}$
- C
$\phi$
- D
$\text{A}\cap\text{B}$
Answer: A.
View full solution →Suppose $A_1, A_2, ..., A_{30}$ are thirty sets each having $5$ elements and $B_1, B_2, ...,$ Bn are $n$ sets each with $3$ elements$,$ let $\bigcup\limits_{\text{i}=1}^{30}\text{A}_\text{i}=\bigcup\limits_{\text{j}=1}^\text{n}\text{B}_\text{j}=\text{S}$ and each element of $S$ belongs to exactly $10$ of the $A_i ’s$ and exactly $9$ of the $B, 'S.$ then $n$ is equal to.
Answer: C.
View full solution →Let $F_1$ be the set of parallelograms$, F_2$ the set of rectangles$, F_3$ the set of rhombuses$, F_4$ the set of squares and $F_5$ the set of trapeziums in a plane. Then $F_1$ may be equal to$,$
- A
$\text{F}_2\cap\text{F}_3$
- B
$\text{F}_3\cap\text{F}_4$
- C
$\text{F}_2\cup\text{F}_5$
- ✓
$\text{F}_2\cup\text{F}_3\cup\text{F}_4\cup\text{F}_1$
Answer: D.
View full solution →$\text{Q} \cup \text{Z} = \text{Q},$ where Q is the set of rational numbers and Z is the set of integers.
View full solution →If A is any set, then $\text{A} \subset \text{A}.$
View full solution →The sets {1, 2, 3, 4} and {3, 4, 5, 6} are equal.
Given A = {0, 1, 2}, $\text{B} = {\text{x} \in \text{R} | 0 \leq \text{x} \leq 2}.$ Then A = B
View full solution →Let sets R and T be defined as
R = {x $\in$ Z | x is divisible by 2}
T = {x $\in$ Z | x is divisible by 6}. Then $\text{T} \subset \text{R}.$
View full solution →If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.
a is less that 6 and $\text{a} \in \text{Y}$
View full solution →If Y = {1, 2, 3, ... 10}, and a represents any element of Y, write the following sets, containing all the elements satisfying the given conditions.
$\text{a} \in \text{Y}$ but $\text{a}^2 \notin \text{Y}.$
View full solution →Write the following sets in the roaster from.
C = {x | x is a positive factor of a prime number p}.
If X = {1, 2, 3}, if n represents any member of X, write the following sets containing all numbers represented by.
n - 1.
Given that N = {1, 2, 3, ..... , 100}. Then write.
The subset of N whose element are perfect square numbers.
A, B and C are subsets of Universal Set U. If A = {2, 4, 6, 8, 12, 20} B = {3, 6, 9, 12, 15}, C = {5, 10, 15, 20} and U is the set of all whole numbers, draw a Venn diagram showing the relation of U, A, B and C.
Write the following sets in the roaster form:
$\text{E}=\Big\{\text{w}|\frac{\text{w}-2}{\text{w}+2}=3,\text{w}\in\text{R}\Big\}$
View full solution →If $Y = x | x$ is a positive factor of the number $2^{p - 1} (2^p - 1),$ where $2^p - 1$ is a prime number.Write $Y$ in the roaster form.
View full solution →For all sets A, and B, $\text{A}\cup(\text{B}-\text{A})=\text{A}\cup\text{B}.$
View full solution →In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students play both the games. Find the number of students who play neither?
Let $\text{T}=\Big\{\text{x}|\frac{\text{x}+5}{\text{x}-7}-5=\frac{4\text{x}-40}{13-\text{x}}\Big\}.$ Is T an empty set? Justify your answer.
View full solution →If A and B are subsets of the universal set U, then show that.
$\text{A} \subset \text{A} \Leftrightarrow \text{A}\cap\text{B}=\text{B}$
View full solution →The set $\{\text{x} \in \text{R} : 1 \leq \text{x} < 2\}$ can be written as ______________.
View full solution →Power set of the set A = {1, 2} is ______________.
If A and B are finite sets such that $\text{A}\subset\text{B},$ then $\text{n} (\text{A} \cup \text{B})$ = ______________.
View full solution →If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}, A = \{1, 2, 3, 5\}, B = \{2, 4, 6, 7\}$ and $C = \{2, 3, 4, 8\}.$ Then
- $(\text{B} \cup \text{C})'$ is $............$
- $(C - A)'$ is $............$
View full solution →Given the sets A = {1, 3, 5}. B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Then the universal set of all the three sets A, B and C can be ______________.
Match the following sets for all sets $A, B$ and $C.$
| $(i)$ |
$((\text{A}'\cup\text{B}')-\text{A})'$ |
$(a)$ |
$\text{A} - \text{B}$ |
| $(ii)$ |
$[\text{B}'\cup(\text{B}'-\text{A})]'$ |
$(b)$ |
$\text{A}$ |
| $(iii)$ |
$(\text{A} - \text{B}) - (\text{B} - \text{C})$ |
$(c)$ |
$\text{B}$ |
| $(iv)$ |
$(\text{A}-\text{B})\cap(\text{C}-\text{B})$ |
$(d)$ |
$(\text{A}\times\text{B})\cap(\text{A}\times\text{C})$ |
| $(v)$ |
$\text{A}\times(\text{B}\cap\text{C})$ |
$(e)$ |
$(\text{A}\times\text{B})\cup(\text{A}\times\text{C})$ |
| $(vi)$ |
$\text{A}\times(\text{B}\cup\text{C})$ |
$(f)$ |
$(\text{A}\cap\text{C})-\text{B}$ |
View full solution →For all sets A, B and C, show that $(\text{A} - \text{B}) \cap (\text{C} - \text{B}) = \text{A} - (\text{B} \cup \text{C})$
Determine whether each of the statement in Exercises 13 - 17 is true or false. Justify your answer.
View full solution →Let A, B and C be sets. Then show that $\text{A}\cap(\text{B}\cup\text{C})=(\text{A}\cap\text{B})\cup(\text{A}\cap\text{C}).$
View full solution →In a survey of 200 students of a school, it was found that 120 study Mathematics, 90 study Physics and 70 study Chemistry, 40 study Mathematics and Physics, 30 study Physics and Chemistry, 50 study Chemistry and Mathematics and 20 none of these subjects. Find the number of students who study all the three subjects.
In a town of $10,000$ families it was found that $40\%$ families buy newspaper $A, 20\%$ families buy newspaper $B, 10\%$ families buy newspaper $C, 5\%$ families buy $A$ and $B, 3\%$ buy $B$ and $C$ and $4\%$ buy $A$ and $C.$ If $2\%$ families buy all the three newspapers. Find
- The number of families which buy newspaper $A$ only.
- The number of families which buy none of $A, B$ and $C.$
View full solution →