Sample QuestionsSets questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Let
$\begin{aligned} \xi & =\{x \mid x \in N, x \text { is a factor of } 144\}, \quad A=\{x \mid x \in N, x \text { is a factor of } 24\}, \\ B & =\{x \mid x \in N, x \text { is a factor of } 36\}, \quad C =\{x \mid x \in N, x \text { is a factor of } 48\} .\end{aligned}$
$A -( B \cap C )$
View full solution →Let
$\begin{aligned} \xi & =\{x \mid x \in N, x \text { is a factor of } 144\}, \quad A=\{x \mid x \in N, x \text { is a factor of } 24\}, \\ B & =\{x \mid x \in N, x \text { is a factor of } 36\}, \quad C =\{x \mid x \in N, x \text { is a factor of } 48\} .\end{aligned}$
$B \cap C ^{\prime}$
View full solution →Let
$\begin{aligned} \xi & =\{x \mid x \in N, x \text { is a factor of } 144\}, \quad A=\{x \mid x \in N, x \text { is a factor of } 24\}, \\ B & =\{x \mid x \in N, x \text { is a factor of } 36\}, \quad C =\{x \mid x \in N, x \text { is a factor of } 48\} .\end{aligned}$
$A \cap B ^{\prime}$
View full solution →Let
$\begin{aligned} \xi & =\{x \mid x \in N, x \text { is a factor of } 144\}, \quad A=\{x \mid x \in N, x \text { is a factor of } 24\}, \\ B & =\{x \mid x \in N, x \text { is a factor of } 36\}, \quad C =\{x \mid x \in N, x \text { is a factor of } 48\} .\end{aligned}$
$A \cup C$
View full solution →Let
$\begin{aligned} \xi & =\{x \mid x \in N, x \text { is a factor of } 144\}, \quad A=\{x \mid x \in N, x \text { is a factor of } 24\}, \\ B & =\{x \mid x \in N, x \text { is a factor of } 36\}, \quad C =\{x \mid x \in N, x \text { is a factor of } 48\} .\end{aligned}$
$B \cup C$
View full solution →Let $A=\{b, c, d, e\}$ and $B=\{d, e, f, g\}$ be two subsets of the universal set $\xi=\{b, c, d$, $e, f, g\}$. Then, verify the following :
$( A \cap B )^{\prime}=\left( A ^{\prime} \cup B ^{\prime}\right)$
View full solution →Let $A=\{b, c, d, e\}$ and $B=\{d, e, f, g\}$ be two subsets of the universal set $\xi=\{b, c, d$, $e, f, g\}$. Then, verify the following :
$( A \cup B )^{\prime}=\left( A ^{\prime} \cap B ^{\prime}\right)$
View full solution →Let $A=\{a, b, c, d, e\}, B=\{a, c, e, g\}$ and $C=\{b, e, f, g\}$. Then verify the following identities :
$A \cap( B \cup C )=( A \cap B$ ) $\cup(A \cap C)$
View full solution →Let $A=\{a, b, c, d, e\}, B=\{a, c, e, g\}$ and $C=\{b, e, f, g\}$. Then verify the following identities :
$A \cup( B \cap C )=( A \cup B$ ) $\cap(A \cup C)$
View full solution →Let $A=\{a, b, c, d, e\}, B=\{a, c, e, g\}$ and $C=\{b, e, f, g\}$. Then verify the following identities :
$A \cap( B \cap C )=( A \cap B$ ) $\cap C$
View full solution →The pair is equivalent set :
$G =\{x: x$ is an integer, $-3 < x<3\}$ and $H =\{x: x$ is a factor of 16$\}$.
View full solution →The pair is equivalent set :
$E =\{x: x$ is a natural number, $x<4\}$ and $F =\{x: x$ is a whole number, $x<3\}$.
View full solution →The pair is equivalent set :
$C =\{x: x+2=2\}$ and $D =\phi$.
View full solution →The pair is equivalent set :
$A =\{2,3,5,7\}$ and $B =\{x: x$ is a whole number, $x \leq 4\}$.
View full solution →Consider the following sets :
$\begin{array}{l}
A=\{x: x \in N, x \text { is a factor of } 3\} \\
B=\{x: x \in N, x \text { is a factor of } 5\} \\
C=\{x: x \in N, x \text { is a factor of } 9\}
\end{array}$
1. $A \cap B=$ ?
(a) $\{x: x \in N, x$ is a factor of 3 or 5$\}$ $\quad$ (b) $\{x: x \in N, x$ is a factor of both 3 and 5\}
(c) $\{x: x \in N, x$ is a factor of 15$\}$ $\quad$ (d) Both (b) and (c)
2. $A \cup B=$ ?
(a) $\{x: x \in N, x$ is a factor of either 3 or 5$\}$ $\quad$ (b) $\{x: x \in N, x$ is a factor of 3 or 5 or both $\}$
(c) $\{x: x \in N, x$ is a factor of 15$\}$ $\quad$ (d) $\{x: x \in N, x$ is a factor of both 3 and 5$\}$
3. $A \cup C=$ ?
(a) $\{x: x \in N, x$ is a factor of 3$\}$ $\quad$ (b) $\{x: x \in N, x$ is a factor of 9$\}$
(c) $\{x: x \in N, x$ is a factor of 27$\}$ $\quad$ (d) None of these
4. $A \cap C=$ ?
(a) $\{x: x \in N, x$ is a factor of 3$\}$ $\quad$ (b) $\{x: x \in N, x$ is a factor of 9$\}$
(c) $\{x: x \in N, x$ is a factor of 27\} $\quad$ (d) None of these
5. How many of the following statements are true:
I. $A \subset B$ II. $A \subseteq C$ III. $B \subseteq A$ IV. $C \subseteq A$
(a) Nil $\quad$ (b) One
(c) Two $\quad$ (d) All
View full solution →The minimum number of subsets a non-empty set has is 2 __________ .
Equal sets are always equivalent __________ .
Two sets A and B are said to be equal if $n(A)=n(B)$ __________ .
View full solution →The power set of a set containing 3 elements, has 6 elements __________ .
$\{x: x+4=4\}$ is a singleton set. __________ .
View full solution →The set of all possible subsets of a set is called its __________ .
If A is a subset of B , then B is a __________ of A.
$x \in A \cup B , \Rightarrow x \in A$ __________ $x \in B$ (and/or)
View full solution →If $\xi=\{a, b, c, d, e, f\}$ and $A =\{b, d, e\}$, then $A ^{\prime}=$ __________ .
View full solution →If $A =\{1,2,3\}$ and $B =\{1,2,3,4\}$, then $A - B =$ __________ .
View full solution →Which one of the following is a correct statement?
- A
$\{a\} \in\{a, b, c\}$
- B
$a \subseteq\{a, b, c\}$
- C
$a \in\{\{a\}, b\}$
- ✓
Answer: D.
View full solution →Which one of the following is a correct statement?
- A
$\phi=0$
- B
$\phi=\{0\}$
- C
$\phi=\{\phi\}$
- ✓
$\phi=\{ \}$
Answer: D.
View full solution →If $A=\{a, b\}$, then the power set of $A$ is
- A
$\left\{a^b, b^a\right\}$
- B
$\left\{a^2, b^2\right\}$
- C
$\{\phi,\{a\},\{b\}\}$
- ✓
$\{\phi,\{a\},\{b\},\{a, b\}\}$
Answer: D.
View full solution →The number of all possible proper subsets of $\{2,3,5\}$ are
Answer: C.
View full solution →If a finite set S contains $n$ elements, then the number of non-empty proper subsets of $S$ is
Answer: D.
View full solution →