(b) The sets A and B are having elements 10 and 8,n(A ∩ B) =2, the n(A ∪B) is _______

(c) A set Z contains 4 elements, and then the number of elements in the Power set of Z will be ______

(d) The set Z={x: x

(2) Set of even prime numbers is not an null set

(3) {

(4) {

(5) The set of months of a year is a finite set

(6) {0,1, 2, 3 ...} is a finite set

(7) {1, 2, 3 ... 999} is an infinite set

(8) The set of positive integers greater than 99 is an infinite set

(9) The set of lines which are parallel to the

(10) The set of letters in the English alphabet is a finite set

(11) The set of natural numbers under 200 which are multiple of 7 is finite set

(12) The set of animals living on the earth is a finite set

(13) The set of circles passing through the origin (0, 0) is a finite set

(14) The set A = {-2, -3}; B = {

(15) The set P = {

(16) {2, 3, 4} ⊂ {1, 2, 3, 4, 5}

(17) {

(18) {

(19) {

(20) {

(21) {

(22) {

(23) {

(24) {

(25) {1, 2, 3} ⊂{1, 3, 5}

(26) {

(27) {

(28) {

(29) If

(30) If A ⊂ B and B ∈ C, then A ∈ C

(31) If A ⊂ B and B ⊂ C, then A ⊂ C

(32) If A ⊄ B and B ⊄ C, then A ⊄ C

(33) If

(34) If A ⊂ B and

- T
- T
- F
- F
- T
- F
- F
- T
- T
- T
- T
- T
- F
- T
- F
- T
- T
- F
- F
- F
- T
- T
- F
- T
- F
- T
- F
- T
- F
- F
- T
- F
- F
- T

Write the following sets in roster form:

(1) U = {

(2) V = {

(3) W = {

(4) X = {

(5) Y= The set of all letters in the word MATHEMATICS.

(6) Z= The set of all letters in the word INTEGRATION.

1. If U = {1,2,3, 5, 7, 9, 11}, V = {7, 9, 11, 13}, W = {11, 13, 15} and X = {15, 17,19,21,23}; find

(i) U ∩ V

(ii) V ∩ W

(iii) U ∩ W ∩ X

(iv) U ∩ W

(v) V ∩ X

(vi) U ∩ (V ∪ W)

(vii) U ∩ (V ∪ X)

(viii) (U ∩ V) ∩ (V ∪ W)

(ix) (U ∪ X) ∩ (V ∪ W)

2.If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20},

C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find

(i) A – B

(ii) A – C

(iii) A – D

(iv) B – A

(v) C – A

(vi) D – A

(vii) B – C

(viii) B – D

(ix) C – B

(x) D – B

(xi) C – D

Let S be the set of people who speak Spanish, and

E be the set of people who speak English

∴

We know that:

∴ 400 = 250 + 200 –

⇒ 400 = 450 –

⇒

∴

Thus, 50 people can speak both Spanish and English.

2. If P and Q are two sets such that P has 40 elements, P ∪Q has 60 elements and P ∩Q has 10 elements, how many elements does Y have?

It is given that:

We know that:

∴ 60 = 40 +

∴

Thus, the set Q has 30 elements.

(b) V={x: x is positive integer less than 1000 and divisible by 7 but not by 11} , n(V)=?

(c) P={x: x is positive integer less than 1000 and divisible by 7 and 11} , n(P)=?

(d) Q={x: x is positive integer less than 1000 and divisible by either 7 or 11} , n(Q)=?

(e) A={x: x is positive integer less than 1000 and divisible by exactly one of 7 or 11} , n(A)=?

(f ) B={x: x is positive integer less than 1000 and divisible by neither 7 nor 11} , n(B)=?

(g) C={x: x is positive integer less than 1000 and have distinct digits} , n(C)=?

(h) D={x: x is positive integer less than 1000 and have distinct digits and even} , n(D)=?

- 142
- 130
- 12
- 220
- 208
- 779
- 738
- 373

(A) X

(B) Y

(C) φ

(D) X ∩ Y

2.For all sets A and B, A – (A ∪ B) is equals to?

(A) A ∩ B

(B) A ∪ Β′

(C) A - B

(D) None of the above

3.Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are.

(A) 6,7

(B) 6,3

(C) 3,6

(D) 7,6

Solutions

1. C

2. B

3. B

**Notes**- Introduction
- Methods of representing a set
- Types of sets
- Subset
- Subset
- Subset of set of the real numbers
- Interval as subset of R Real Number
- Power Set
- Universal Set
- Venn diagram
- Operation on Sets
- Cardinality of Sets
- Set Theory Symbols

**Assignments**