## Mathematics - Sets

## CBSE Class 11

## NCERT Exercise 1.2

**Q1. Which of the following are examples of the null set**

**(i) Set of odd natural numbers divisible by 2**

**Answer**: Yes

**(ii) Set of even prime numbers**

**Answer**: No

**(iii) { x : x is a natural numbers, x < 5 and x > 7 }**

**Answer**: Yes

**(iv) { y : y is a point common to any two parallel lines}**

**Answer**: Yes

**Q2. Which of the following sets are finite or infinite**

**(i) The set of months of a year**

**Answer**: Finite

**(ii) {1, 2, 3, . . .}**

**Answer**: Infinite

**(iii) {1, 2, 3, . . .99, 100}**

**Answer**: Finite

**(iv) The set of positive integers greater than 100**

**Answer**: Infinite

**(v) The set of prime numbers less than 99**

**Answer**: Finite

**Q3. State whether each of the following set is finite or infinite:**

**(i) The set of lines which are parallel to the x-axis**

**Answer**: Infinite

**(ii) The set of letters in the English alphabet**

**Answer**: Finite

**(iii) The set of numbers which are multiple of 5**

**Answer**: Infinite

**(iv) The set of animals living on the earth**

**Answer**: Finite

**(v) The set of circles passing through the origin (0,0)**

**Answer**: Infinite

**Q4. In the following, state whether A = B or not:**

**(i) A = { a, b, c, d } B = { d, c, b, a }**

**Answer**: A = B

**(ii) A = { 4, 8, 12, 16 } B = { 8, 4, 16, 18}**

**Answer**: A ≠ B

**(iii) A = {2, 4, 6, 8, 10} B = { x : x is positive even integer and x ∈ 10}**

**Answer**: A = B

**(iv) A = { x : x is a multiple of 10}, B = { 10, 15, 20, 25, 30, . . . }**

**Answer**: A ≠ B

**Q5. Are the following pair of sets equal ? Give reasons.**

**(i) A = {2, 3}, B = {x : x is solution of x² + 5x + 6 = 0}**

**Answer**: x² + 5x + 6 = 0

⇒ x² + 3x + 2x + 6 = 0

⇒ (x + 2)(x + 3) = 0

⇒ x = -2 or x = -3

Clearly, A ≠ B

**(ii) A = { x : x is a letter in the word FOLLOW}**

**B = { y : y is a letter in the word WOLF}**

**Answer**:

A = { x : x is a letter in the word FOLLOW} = {F, O, L, W}

B = { y : y is a letter in the word WOLF} = {W, O, L, F}

Since every member of set A is in B and every element of set B is in A.

⇒ A = B

**Q6. From the sets given below, select equal sets :**

**A = { 2, 4, 8, 12},**

**B = { 1, 2, 3, 4},**

**C = { 4, 8, 12, 14},**

**D = { 3, 1, 4, 2}**

**E = {–1, 1},**

**F = { 0, a},**

**G = {1, –1},**

**H = { 0, 1}**

**Answer**:

Clearly n(G) = n(E) = n(H) = n(F) = 2

∴ Sets G, E, H and F are equivalent sets.

Also n(A) = n(B) = n(C) = n(D) = 4

∴ Sets A, B, C and D are equivalent sets.

Since every element of B is in D, and every element of D is in B.

∴ D = B

Since every element of E is in G, and every element of G is in E.

∴ E = G

☛See also:

Special Mathematical Constants

SETS (Unit Test Paper)

Maths Annual Test Paper (2018-19)

## No comments:

## Post a Comment

We love to hear your thoughts about this post!

Note: only a member of this blog may post a comment.