SETS :Practice set 1.2

Practice set 1.2

Question 1:

Decide which of the following are equal sets and which are not ?

Justify your answer.

A = { x | 3 x -1 = 2}

B = { x | x is a natural number but x is neither prime nor

composite}

C = { x | x ∈ N, x < 2}

ANSWER:

Since, A = {x | 3x - 1 = 2} = {1};

B = {x | x is a natural number but x is neither prime nor composite}

= {1}; and

C = {x | x ∈ N, x < 2} = {1}

So, A = B = C

Question 2:

Decide whether set A and B are equal sets. Give reason for your

answer.

A = Even prime numbers

B = { x | 7 x -1 = 13}

ANSWER:

Since, A = Even prime numbers = {2}; and

B = {x | 7x −1 = 13} = {2}

So, A = B

hence, A and B are equal sets.

Question 3:

Which of the following are empty sets ? why ?

( i ) A = { a | a is a natural number smaller than zero.}

( ii ) B = { x | x 2 = 0}

( iii ) C = { x | 5 x - 2 = 0, x ∈ N}

ANSWER:

(i) A = {a | a is a natural number smaller than zero.} = { }

So, A is an empty set.

(ii) B = {x | x2 = 0} = {0}

So, B is not an empty set.

(iii) C = {x | 5x − 2 = 0, x ∈ N} = { }

So, C is an empty set.

Question 4:

Write with reasons, which of the following sets are finite or infinite.

( i ) A = { x | x < 10, x is a natural number}

(ii) B = { y | y < -1, y is an integer}

(iii) C = Set of students of class 9 from your school.

(iv) Set of people from your village.

(v) Set of apparatus in laboratory

(vi) Set of whole numbers

(vii) Set of rational number

ANSWER:

(i) A = {x | x < 10, x is a natural number} = {1, 2, 3, 4, 5, 6, 7, 8, 9}

So, A is a finite set.

(ii) B = {y | y < − 1, y is an integer} = {..., − -5, − -4, − -3, − -2}

So, B is an infinite set.

(iii) C = Set of students of class 9 from your school.

Since, the number of elements of set C is countable number.

So, C is a finite set.

(iv) D = Set of people from your village.

Since, the number of elements of set D is countable number.

So, D is a finite set.

(v) E = Set of apparatus in laboratory

Since, the number of elements of set E is countable number.

So, E is a finite set.

(vi) F = Set of whole numbers = {0,1, 2, 3, 4, ...}

So, F is an infinite set.

(vii) G = Set of rational number

Since, the number of elements of set G is infinite.

So, G is an infinite set.