Union

Q.

From 50 students taking examinations in Mathematics, Physics and Chemistry, each of the student has passed in atleast one of the subjects, 37 passed in Mathematics, 24 in Physics and 43 in Chemistry. At most 29 passed in Mathematics and Chemistry, at most 19 passed in Mathematics and Physics and at most 20 in Physics and Chemistry. Find the largest possible number of students that could have passed in all three examinations.

Q.

If n(A)=2, n(B)=2 . What is the total number of relations from A to B?

1. 4

2. 16

3. 12

4. 32

Q.

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}, verify that

(i) $(A\cup B{)}^{\prime }=A^{\prime }\cap B^{\prime }$

(ii) $(A\cap B{)}^{\prime }=A^{\prime }\cup B^{\prime }$

Q. 54.Two finite sets have p and q elements respectively. The total number of subsets of first set is 224 more than the total number of subsets of second set. Find the values of p and q.

Q.

If n(A) = 3 and n(B) =4 then find the number of elements in the power set of A × B

1. 8

2. 24

3. 4096

4. 64

Q.

If set A has 4 elements and B = {5, 6}, then the number of elements in A x B are

1. 9

2. 7

3. 10

4. 8

Q. 12. Two finite sets A and B have p and q elements respectively (p>q). The number of subsets of the power set of A is 240 more than the total number of subsets of power set of B. Then p+q is ________.

Q. 6. IfA 3, 5, 7, 9, 11 ), B 17, 9, 11, 13], C 111, 13, 15and D(ii) BnC(v) BnDA(15, 17); find(i) An Biv) An CVi1(x) (Au D)n Bu C)(ii) AnCn D(vi) An(BU C)V1(vii) AnD(viii)(BUD)(i)(AB)n(BUC)Vill

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 people like both coffee and tea?

Q. If R is a relation from a finite set A having m elements of a finite set B having n elements, then the number of relations from A to B is

(a) 2^mn
(b) 2^mn − 1
(c) 2mn
(d) mⁿ

Q. A survey shows that in a city, $45$% citizens like tea, whereas $65$% citizens like coffee. If $x$% like both tea and coffee, then

1. $x=45$
2. $x=10$
3. $10\le x\le 45$
4. $45\le x\le 55$

Q.

Which of the following is a null set?

1. $X=\left\{\phi \right\}$

2. $Y=\left\{X:X\ge 3\right\}$

3. $Z=\left\{X:X<1\mathrm{and}X>1\right\}$

4. $A=\left\{X:X\ge 1\mathrm{and}X\le 1\right\}$

Q. If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find (i) A ∪ B (ii) A ∪ C (iii) B ∪ C (iv) B ∪ D (v) A ∪ B ∪ C (vi) A ∪ B ∪ D (vii) B ∪ C ∪ D

Q.

In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then persons travelling by car or bus is

1. 60 percent

2. 70 percent

3. 80 percent

4. 40 percent

Q. no. of elements in the domain of combination of 7-x with x-5

Q. Describe the following sets in set-builder form:
(i) A = {1, 2, 3, 4, 5, 6};
(ii) $B=\left\{1,\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.,\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.,\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.,\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.,...\right\};$
(iii) C = {0, 3, 6, 9, 12, ...};
(iv) D = {10, 11, 12, 13, 14, 15};
(v) E = {0};
(vi) {1, 4, 9, 16, ..., 100}
(vii) {2, 4, 6, 8 .....}
(viii) {5, 25, 125 625}

Q. If $A=\{x:x$ is a natural number $\},B=\{x:x$ is an even natural number$\}C=\{x:x$ is an odd natural number$\}$ and $D=\{x:x$ is a prime number $\},$ find
(i) $A\cap B$

Q. Find the union of each of the following pairs of sets: (i) X = {1, 3, 5} Y = {1, 2, 3} (ii) A = { a , e , i , o , u } B = { a , b , c } (iii) A = { x : x is a natural number and multiple of 3} B = { x : x is a natural number less than 6} (iv) A = { x : x is a natural number and 1 < x ≤ 6} B = { x : x is a natural number and 6 < x < 10} (v) A = {1, 2, 3}, B = Φ

Q.

If A = {x: x is a natural number}

B = {x: x is even natural number}

C = {x: x is prime number}

Then (A ∪ B)∩ C =

1. A

2. A ∩ B

3. B

4. C

Q. If the set A has p elements, B has q elements, then the number of elements in A × B is

(a) p + q
(b) p + q + 1
(c) pq
(d) p²

Q. If A = {1, 2, 3} and B = {x, y}, then the number of functions that can be defined from A into B is

(a) 12
(b) 8
(c) 6
(d) 3

Q. 69. how to find conjugate of a complex number

Q. Prove that: (i) (A ∪ B) × C = (A × C) ∪ (B × C) (ii) (A ∩ B) × C = (A × C) ∩ (B×C)

Q.

Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b²}. Are the following true?

(i) (a, a) ∈ R, for all a ∈ N

(ii) (a, b) ∈ R, implies (b, a) ∈ R

(iii) (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R.

Justify your answer in each case.

Q. Show that for any sets A and B, A = (A ∩ B) ∪ (A – B) and A ∪ (B – A) = (A ∪ B)

Q. Let A and B be two sets having 3 and 6 elements respectively. Write the minimum number of elements that $A\cup B$ can have.

Q.

If A = {1, 2, 3, 4}, B = {3, 4} and C = {2, 3} then n ((A ∩ B x C)

1. 8

2. 2

3. 4

4. 16

Q. If A and B are two sets such that A ⊂ B, then what is A ∪ B?

Q.

1. all real numbers except 2

2. all real numbers except 4

3. all real numbers except 2 and -2

4. all real numbers except 4 and -4

Q. Suppose $A_1,A_2,...A_{30}$ are thirty sets each having $5$ elements and $B_1,B_2,...B_n$ are $n$ sets each with $3$ elements. Let $\bigcup _{i=1}^{30}{A}_i=\bigcup _{i=1}^n{B}_i=S$ and each element of $S$ belongs to exactly $10$ of the $A_i$ and exactly $9$ of the $B_i$. then

1. $n$ is an odd number
2. $n$ is an odd prime number
3. $n$ has two prime factors
4. $n$ has only one prime factor