Difference of Two Sets

Q. Let $A=\{0,1,2,3,4,5,6,7\}$. Then the number of bijective functions $f:A\to A$ such that $f\left(1\right)+f\left(2\right)=3-f\left(3\right)$ is equal to

Q. In a group of $50$ people, $35$ speak Hindi and $25$ speak both English and Hindi. Then how many people speak only English ? (Assuming each person speaks at least one language)

1. $16$
2. $25$
3. $15$
4. $10$

Q.

For any set $A,\left(A\right)$is equal to

1. $A$

2. $A$

3. $\varphi$

4. None of these

Q.

The symmetric difference of A and B is not equal to

1. $(A\cup B)-(A\cap B)$

2. $(A-B)\cap (B-A)$

3. $(A-B)\cup (B-A)$

4. {$(A\cup B)-A$} $\cup$ {$(A\cup B)-B$}

Q. If $n\left(A\right)=50,n\left(B\right)=20,n(A\cap B)=10,$ then $n\left(A\Delta B\right)=$

1. $60$
2. $50$
3. $40$
4. $70$

Q.

Consider the following relations

$1.A-B=A-(A\cap B)$

$2.A=(A\cap B)\cup (A-B)$

$3.A-(B\cup C)=(A-B)\cup (A-C)$

Which of these is/are correct?

1. $1$ and $3$

2. $2$ only

3. $2$ and $3$

4. $1$ and $2$

Q.

For any two sets A and B, prove that :

A' - B' = B- A

Q. $\mathrm{If}{A}^{-1}=\left[\begin{array}{ccc}3& -1& 1\\ -15& 6& -5\\ 5& -2& 2\end{array}\right]\mathrm{and}B=\left[\begin{array}{ccc}1& 2& -2\\ -1& 3& 0\\ 0& -2& 1\end{array}\right],\mathrm{find}{\left(AB\right)}^{-1}.$

Q. If two sets $A$ and $B$ are such that $n\left(A\right)=20$, $n(A\cap B)=4$, and $n(A\cup B)=42$, then

1. $n\left(B\right)=22$
2. $n(B-A)=22$
3. $n\left(B\right)=26$
4. $n(A-B)=16$

Q. If R $⊑$ A $\times$ B and S $⊑$ B $\times$ C be two relations, then $(SoR{)}^{-1}$ is equal to

1. RoS
2. None of these
3. $S^{-1}o{R}^{-1}$
4. $R^{-1}o{S}^{-1}$

Q.

Let A and B be sets. Show that $f:A\times B\to B\times A$ such that f(a, b)=(b, a) is bijective function.

Q. If n(A) = 7; n(B) = 9, n(A ∩ B) = 4; then n[(A × B) ∩ (B × A)] is equal to

Q. The H.C.F. and L.C.M. of two numbers are $8$ and $96$ respectively. If one number is $24,$ the other number is

1. $12$
2. $16$
3. $32$
4. $48$

Q.

Let A and B be two sets such that n(A)=20, n(AUB)=42, n(AintersectionB)=4.

Find i) n(B)

ii) n(A-B)

iii) n(B-A)

Q. Let $A=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 1\\ 0& -2& 4\end{array}\right]$ and $I$ be an identity matrix of order $3.$ If $A^{-1}=\frac{1}{6}(A^2+cA+dI)$ where $c$ and $d$ are real numbers, then the value of $c+d$ is

1. $11$
2. $5$
3. $0$
4. $1$

Q. In a class of $70$ students, $38$ students like physics, $21$ students like mathematics and $15$ students like both the subjects, then the number of students who like neither of the subjects is

1. $27$
2. $24$
3. $11$
4. $26$

Q.

The number of surjections from $A=\left\{1,2,\dots .n\right\},n\ge 2$ onto $B=\left\{a,b\right\}$ is

1. ${}^{n}P_2$

2. $2^n-2$

3. $2^n-1$

4. None of these

Q.

If A and B are two sets such that $A\subset B$, then write B' - A' in terms of A and B.

Q.

The symmetric difference of A = {1, 2, 3 } and {3, 4, 5} is ___.

1. {1, 2}

2. {1, 2, 4, 5}

3. {2, 5, 1, 4, 3}

4. {4, 3}

Q. If $A=\{x:x\in R,0<x<2\}$, $B=\{x:x\in R,1<x\le 3\}$, then $A-B=$

1. $(0,2)$
2. $(1,3]$
3. $(0,1]$
4. $(0,1)$

Q. Let $S_1,S_2$ and $S_3$ be three sets defined as
$S_1=\text{{}z\in C:|z-1|\le \sqrt{2}\text{}}$
$S_2=\text{{}z\in C:\text{Re}\left((1-i)z\right)\ge 1\text{}}$
$S_3=\text{{}z\in C:\text{Im}\left(z\right)\le 1\text{}}$
Then the set $S_1\cap S_2\cap S_3$

1. Has infinitely many elements
2. Has exactly two elements
3. Has exactly three elements
4. Is a singleton

Q. Let A = [$-$1, 1]. Then, discuss whether the following functions from A to itself are one-one, onto or bijective:

(i) f(x) = $\frac{x}{2}$ (ii) g(x) = |x| (iii) h(x) = x² [NCERT EXEMPLAR]

Q. If two sets $A$ and $B$ are such that $(A-B)=A$, then $A\cap B=$

1. $\varphi$
2. $A$
3. $B$
4. $A\cup B$

Q.

If A, B, C are three sets such that $A\subset B$, then prove that $C-B\subset C-A$

Q. If $n\left(A\right)=50,n(A\cup B)=80,n(A\cap B)=30$, then $n(B–A)=$

1. $20$
2. $30$
3. $40$
4. $23$

Q.

What is the symmetric difference of two sets $A$ and $B$?

Q. If the functions $f$ and $g$ are defined on $R\to R$ such that
$f\left(x\right)=\{\begin{array}{c}0,\text{if}x\text{is rational}\\ x,\text{if}x\text{is irrational}\end{array}$ and
$g\left(x\right)=\{\begin{array}{c}0,\text{if}x\text{is irrational}\\ x,\text{if}x\text{is rational}\end{array},$
then $(f-g)\left(x\right)$ is

1. a bijective function
2. neither a one-one nor an onto function
3. a one-one but not an onto function
4. an onto but not a one-one function

Q. If $A$ and $B$ are two sets, then $\frac{A}{\left(\frac{A}{B}\right)}$ is equal to
$(\frac{A}{B}$ represents the difference of the sets $A$ and $B$ in this order.$)$

1. $A$
2. $A\cap B$
3. $A\cup B$
4. $B^{\prime }$

Q. W is a set of whole numbers and Z is a set of integers. Then, Z-W is a set of

1. Positive Integers
2. Negative Integers
3. Natural Numbers
4. Real Numbers

Q. Let A and B be two sets in the same universal set. Then A - B =

1. $A\cap B$
2. $A\cap B$
3. $A\cap B$
4. $A-(A\cap B)$