Q1 of 43 Page 6

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}

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.


More from this chapter

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4

Write the following sets using listing method.

i. All months in the Indian solar year.


ii. Letters in the word ‘COMPLEMENT’.


iii. Set of human sensory organs.


iv. Set of prime numbers from 1 to 20.


v. Names of continents of the world.

 5

Write the following sets using rule method. We know that in rule method, we do not write the list of elements but write the general element using variable followed by a vertical line or colon and write the property of the variable.

i. A = {1,4,9,16,25,36,49,64,81,100}


ii. B = {6,12,18,24,30,36,42,48}


iii. C = {S, M, I, L, E}


iv. D = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

 2

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

A = Even prime numbers


B = {x| 7x – 1 = 13}

 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}