Practice Set 1.2 Sets Class 9th Mathematics Part I MHB Solution

Practice Set 1.2 Sets Class 9th Mathematics Part I MHB Solution

Practice Set 1.2

Question 1.

Decide which of the following are equal sets and which are not? Justify your answer.

A = {x|3x – 1 = 2}

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

C = {x |x ∈ N, x < 2}


Answer:

We know that two sets A and B are said to be equal, if every element of set A is in set B and every element of set B is in set A. It is symbolically written as A = B.


A = {x|3x – 1 = 2}


⇒ 3x – 1 = 2


⇒ 3x = 2 + 1 = 3


⇒ x = 3/3 = 1


∴ A = {1}


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


We know that 1 is neither prime nor composite and is a natural number.


∴ B = {1}


C = {x |x ∈ N, x < 2}


We know that natural number, N = {0, 1, 2, 3, …}


∴ C = {0, 1}


A = B, B ≠ C, A ≠ C


Ans. A and B are equal sets but B and C (and) A and C are not equal sets.



Question 2.

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

A = Even prime numbers

B = {x| 7x – 1 = 13}


Answer:

We know that two sets A and B are said to be equal, if every element of set A is in set B and every element of set B is in set A. It is symbolically written as A = B.


A = Even Prime Numbers = {2}


B = {x| 7x – 1 = 13}


⇒ 7x – 1 = 13


⇒ 7x = 13 + 1 = 14


⇒ x = 14/7


∴ x = 2


∴ A = B


Ans. Set A and set 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|x2 = 0}

iii. C = {x|5x – 2 = 0, x ∈ N}


Answer:

i. We know that If there is not a single element in the set which satisfies the given condition then it is called a Null set or an Empty set. Empty set is represented by { }.


We know that Natural number, N = {0, 1, 2, … }.


∴ A = {a |a is a natural number smaller than zero} = {}


Ans. A is an empty set.


ii. B = {x|x2 = 0}


⇒ x2 = 0


∴ x = 0


B = {x|x2 = 0} = {0} ≠ {}


Ans. B is not an empty set.


iii. C = {x|5x – 2 = 0, x ∈ N}


⇒ 5x – 2 = 0


⇒ 5x = 2


⇒ x = 5/2


We know that natural number, N = {0, 1, 2,… }


∴ x N


∴ C = {x|5x – 2 = 0, x ∈ N} = {}


Ans. C is an empty set.



Question 4.

Write with reasons, which of the following sets are finite or infinite. We know that if a set is a null set or number of elements are limited and countable then it is called ‘Finite set’ and if number of elements in a set is unlimited and uncountable then the set is called ‘Infinite set’.

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

ii. B = {y |y< -1, 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}


∴ A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}


Ans. A is a finite set.


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


∴ B = {… -5, -4, -3, -2}


Ans. B is an infinite set.


iii. C = {a, b, c, d, e, …}


Ans. C is an infinite set.


iv. D = {Sarpanch, villager1, villager2, …}


Ans. D is an infinite set.


v. E = {Beakers, funnels, chemicals, thermometers, …}


Ans. E is an infinite set.


vi. W = {1, 2, 3, 4, 5, …}


Ans. W is an infinite set.


vii. Q = {(p/q) |p, q ∈ I, q ≠ 0}


Q = {1/2, 1/3, 1/4, …}


Ans. Q is an infinite set.

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