Difference of Sets

Q.

A survey shows that $70\%$ of the Indian like mango whereas $82\%$ like an apple. If $x\%$ of Indian like both mango and apples then

1. $x=52$

2. $52\le x\le 70$

3. $\mathrm{x}=70$

4. $70\le x\le 82$

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

1. $A\cap B^c$
2. $A^c\cap B$
3. $A\cap B$
4. $\text{None of these}$

Q.

Let $A=\left\{1,2,3\right\}$ and $B=\left\{2,3,4\right\}$, then which of the following relations is a function from $A$ to $B$

1. $\left\{(1,2),(2,3),(3,4),(2,2)\right\}$

2. $\left\{(1,2),(2,3),(1,3)\right\}$

3. $\left\{(1,3),(2,3),(3,3)\right\}$

4. $\left\{(1,1),(2,3),(3,4)\right\}$

Q.

Which of the following two sets are equal?

1. $A=\{1,2\}\mathrm{and}B=\left\{1\right\}$

2. $A=\{1,2\}\mathrm{and}B=\{1,2,3\}$

3. $A=\{1,2,3\}\mathrm{and}B=\{2,1,3\}$

4. $A=\{1,2,4\}\mathrm{and}B=\{1,2,3\}$

Q. A survey shows that $73\%$ of the persons working in an office like coffee, whereas $65\%$ like tea. If $x$ denotes the percentage of them, who like both coffee and tea, then $x$ cannot be:

1. $63$
2. $54$
3. $38$
4. $36$

Q. Find, which of the following sets are singleton sets:
$B=\{y:2y+1<3andy\in W\}$

Q. If $A=\{x:x\text{is a multiple of}3\}$ and $B=\{x:x\text{is a multiple of}5\}$, then $A-B=$

1. $A^C\cap B$
2. $A\cap B^C$
3. $A^C\cap B^C$
4. $(A\cap B{)}^C$

Q. The complete solution set of 5x ≥ x² + 6 is

5x ≥ x² + 6 का संपूर्ण हल समुच्चय है

1. [–3, –2]
2. [–3, 2]
3. [2, 3]
4. (2, 3)

Q.

$U=\{x:x\text{is a natural number \&}x\le 10\}$
$A=\{a:a\text{is an even number \&}a\le 10\}$
$B=\{b:b\text{is a prime number \&}b\le 9\}$

Then, $A^c\cap B^c$ is

1. $\{2,4,6,8\}$

2. $\{3,5,7\}$

3. $\{1,9,10\}$

4. $\{2,3,5,7\}$

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 $A=\{x:x\text{is a multiple of 3}\}$ and $B=\{x:x\text{is a multiple of 5}\}$ , then $A-B$ is

1. $\overline{A}$ $\cap$ B

2. A $\cap$ $\overline{B}$ .

3. $\overline{A}$ $\cap$ $\overline{B}$ .

4. $\frac{}{A\cap B}$

Q. If two non-empty sets A and B are such that A ∩ B = B, then

यदि दो अरिक्त समुच्चय A व B इस प्रकार हैं कि A ∩ B = B, तब

1. A ⊂ B
   
2. B ⊂ A
   
3. A = φ
   
4. B = φ
   

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 $A$ and $B$ are disjoint non-empty sets, then $A–(A–B)$ is

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

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. Number of subsets of A = {φ, {φ}} is

A = {φ, {φ}} के उपसमुच्चयों की संख्या है

1. 2
2. Zero
   
   शून्य
3. 1
4. 4

Q. If $W$ is a set of whole numbers and $Z$ is a set of integers. Then, $Z-W$ will be a set of

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

Q. Consider the two sets:
$A=\{m\in R:\text{both the roots of}{x}^2-(m+1)x+m+4=0\text{are real}\}$ and $B=[-3,5).$
Which of the following is not true ?

1. $A-B=(-\infty ,-3)\cup (5,\infty )$
2. $A\cap B=\{-3\}$
3. $B-A=(-3,5)$
4. $A\cup B=R$

Q. A and B are sets such that n(A) = 15 and n(B) = 25 and n(A ∪ B) = 30, then n(A ∩ B) =

A तथा B समुच्चय हैं जबकि n(A) = 15 और n(B) = 25 तथा n(A ∪ B) = 30, तब n(A ∩ B) =

1. 15
2. 10
3. 5
4. 12

Q. Let A and B be two sets in the same universal set. Then A - B is a null set if

1. A and B are disjoint sets
2. A is contained in B
3. B is contained in A
4. A and B are both Null Sets

Q. Let A and B be two sets such that $n\left(A\right)=20,n(A\cup B)=42\text{and}$
$n(A\cap B)=5,$ then $n(B-A)=$

1. $18$
2. $20$
3. $22$
4. $27$

Q. $\text{If}P=\{x:x\in N,10<x<16\},$
$Q=\{y:y\text{is an even number between}8\text{and}20\},$ then
$P-Q=$

1. $\{11,13,15\}$
2. $\{11,14,15\}$
3. $\{12,14\}$

Q. A and B are sets such that n(A) = 15 and n(B) = 25 and n(A ∪ B) = 30, then n(A ∩ B) =

A तथा B समुच्चय हैं जबकि n(A) = 15 और n(B) = 25 तथा n(A ∪ B) = 30, तब n(A ∩ B) =

1. 15
2. 10
3. 5
4. 12

Q.

Venn diagram representation of A - B for 2 sets A & B is

1. 

2. 

3. 

4. 

Q. For any two sets $M\&N,M-N$ is the set of all elements of $M$which are not in $N.$

1. False
2. True

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

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

Q. For two sets $X\&Y,X-Y=$, $\text{and}Y-X=$

1. $X-(X\cap Y)$
2. $X-(X\cup Y)$
3. $Y-(X\cup Y)$
4. $Y-(X\cap Y)$

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

1. $A\cap B$
2. $A\cap B\text{'}$
3. $A\text{'}\cap B$
4. $A-(A\cap B)$

Q. Let A and B be two sets in the same universal set. Then A - B is a null set if

1. A and B are disjoint sets
2. A is contained in B
3. B is contained in A
4. A and B are both Null Sets

Q. For any two sets $A\&B;n(A-B)=$ $\text{and}n(B-A)=$

1. $n\left(A\right)+n(A\cap B)$
2. $n\left(A\right)-n(A\cap B)$
3. $n\left(B\right)-n(A\cap B)$
4. $n\left(B\right)+n(A\cap B)$