Union

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.

In a group of 65 people 40 like cricket, 10 like both cricket and tennis, how like tennis only and not cricket?

Q.

For any two sets A and B, prove that

(i) $B\subset A\cup B$

(ii) $A\cap B\subset A$

(iii) $A\subset B\Rightarrow A\cap B=A$

Q.

Let $\mathrm{n}\left(\mathrm{U}\right)=700,\mathrm{n}\left(\mathrm{A}\right)=200,\mathrm{n}\left(\mathrm{B}\right)=300$ and $\mathrm{n}(\mathrm{A}\cap \mathrm{B})=100$, then $n({\mathrm{A}}^{\mathrm{c}}\cap {\mathrm{B}}^{\mathrm{c}})=$

1. $400$

2. $600$

3. $300$

4. $200$

Q.

Let $A$ and $B$ be the two sets such that $n\left(A\right)=0.16$, $n\left(B\right)=0.14$, $n\left(A\cup B\right)=0.25$.Then $n\left(A\cap B\right)$ is equal to

1. $0.3$

2. $0.5$

3. $0.05$

4. None of these

Q.

The value of $(A\cup B\cup C)$ intersection ( $A$ intersection $B^C$ intersection $C^C$)${}^C$ intersection $C^C$ is,

1. $B\cap C^C$

2. $B^C\cap C^C$

3. $B\cap C$

4. $A\cap B\cap C$

Q.

If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A × B)?

Q. The smallest set $A$ such that $A\cup \{1,2\}=\{1,2,3,5,9\}$ is

1. $\{2,3,5\}$
2. $\{3,5,9\}$
3. $\{1,2,5,9\}$
4. $\{1,2,\}$

Q. Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let R1 be a relation in X given by R1 = {(x, y) : x – y is divisible by 3} and R2 be another relation on X given by R2 = {(x, y): {x, y} ⊂ {1, 4, 7}} or {x, y} ⊂ {2, 5, 8} or {x, y} ⊂ {3, 6, 9}}. Show that R1 = R2.

Q.

Prove that A-(BnC)=(A-B)U (A-C)

Q.

Using properties of sets, show that for any two sets A and B, $(A\cup B)\cap (A\cap B^{\prime })=A.$

Q. If $A=\{2,3,4,8,10\},$ $B=\{3,4,5,10,12\},$ $C=\{4,5,6,12,14\},$ then $(A\cup B)\cap (A\cup C)$ is

1. $\{2,3,4,5,8,10,12\}$
2. $\{2,4,8,10,12\}$
3. $\{3,8,10,12\}$
4. $\{2,8,10,\}$

Q.

In a class $18$ students took Physics, $23$ students took Chemistry and $24$ students took Mathematics of those $13$ took both Chemistry and Mathematics, $12$ took both Physics and Chemistry and $11$ took both Physics and Mathematics. If $6$ students offered all the three subjects, find out how many took exactly one of the three subjects.

Q.

If the sum of three consecutive terms of an A.P is $51$ and the product of last and first term is $273$, then the numbers

1. $21,17,13$

2. $20,16,12$

3. $22,18,14$

4. $24,20,16$

Q. If $A$ is the set of the divisors of $15,B$ is the set of prime numbers less than $10$ and $C$ is the set of even numbers smaller than $9,$ then $(A\cup C)\cap B$ is the set

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

Q.

In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach physics and mathematics. How many teach physics ?

Q. Let $A=\{x:x\text{is a prime factor of}240\}$ and $B=\{y:y\text{is the sum of any two prime factors of}240\}$. Then which of the following options is true?

1. $5\notin A\cap B$
2. $7\in A\cap B$
3. $8\in A\cap B$
4. $8\in A\cup B$

Q.

For any two sets A and B, show that the following statements are equivalent :

(i) $A\subset B$ (ii) $A-B=\varphi$

(iii) $A\cup B=B$ (iv) $A\cap B=A.$

Q. If $A=\{x:x\text{is an even number and}0<x<10\}$ and $B=\{2,3,5,7\}$, then the number of elements in $A\cup B$ is

Q.

Which number should be added to the numbers $13,15,19$ so that the resulting numbers be the consecutive terms of an H.P.?

1. $7$

2. $6$

3. $-6$

4. $-7$

Q. In a class of $80$ students numbered $1$ to $80$, all odd numbered students opt for cricket, students whose numbers are divisible by $5$ opt for football and students whose numbers are divisible by $7$ opt for hockey. The number of students who do not opt any of the three games, is -

1. $13$
2. $24$
3. $28$
4. $52$

Q. The area enclosed by the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ is

1. $3\pi$
2. $\pi$
3. $6\pi$
4. $9\pi$

Q.

In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many like both coffee and tea ?

Q.

Which of the following is/are true?

1. If $A$ is a subset of the universal set $U$, then its complement $A$ is also a subset of $U$.

2. If $U=\left\{1,2,3,\dots ..,10\right\}$ and $A=\left\{1,3,5,7,9\right\}$, then $(A)=A$.

1. Only I is true

2. Only II is true

3. Both I and II are true

4. None of these

Q. Mark the correct alternative in the following question:

If the set A contains 7 elements and the set B contains 10 elements, then the number one-one functions from A to B is

(a) ¹⁰C₇ (b) ¹⁰C₇ $\times$ 7! (c) 7¹⁰ (d)10⁷

Q.

Classify True or False:
The absolute value of an integer is always greater than the integer.

1. True
2. False

Q.

If A and B are two sets such that $n(A\cup B)$ = 50, n(A) = 28 and n(B) = 32, find $n(A\cap B)$.

Q.

If

(A) 0 (B)

(C) not defined (D) 1

Q.

In the matrix, write:

(i) The order of the matrix (ii) The number of elements,

(iii) Write the elements a₁₃, a₂₁, a₃₃, a₂₄, a₂₃

Q. Draw a venn diagram of $A\cup B$