## Problems on set-II

In this page 'Problems on set-II' we are going to see problems on cardinal number, finite-infinite sets, and equal-equivalent sets.

Parents and teachers can guide the students to do the problems on their own. If they are having any doubt they can verify the solutions.

### Problems on set-II

Cardinal number

The following problems are about cardinal number of sets.

1. Find the cardinal number of sets.

(i) A = {x: x=5ⁿ, n∈ℕ and n< 5}

(ii) B = {x: x is a consonant in English Alphabet}

(iii) C = {x: x is an even prime number}

(iv) D = {x: x<0,x∈W}

(v) E = {x:-3 ≤ x ≤ 5, x∈ℤ}

Finite-Infinite sets

The following problems are based on finite-infinite sets.

2. Identify the following as finite or infinite sets.

(i) A= {4,5,6,...}

(ii) B = {0,1,2,3,4....75}

(iii) C ={x: x is an even natural number}

(iv) D = {x: x is a multiple of 6 and x >0}

(v) E = The set of letters in the word, 'ASTRONOMY'.

Solutions

The following problems are based on equal-equivalent sets.

3.Which of the following sets are equivalent?

(i) A = {2,4,6,8,10}, B= {1,3,5,7,9}

(ii) X = {x:x∈ℕ, 1<x<6}, Y={x: x is a vowel in the English Alphabet}

(iii) P = { x: xis a prime number and 5 < x < 23}

Q = {x: x∈W, 0 ≤ x < 5}

4. Which of the following sets are equal?

(i) A= {1,2,3,4}, B= {4,3,2,1}

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

(iii) X= {2,4,6,8}

Y = {x: x is a positive even integer 0 < x < 10}

(iv) P = {x: x is a multiple of 10, x∈ℕ}

Q= {10,15,20,25,30....}

5. From the sets given below, select equal sets.

A= {12,14,18,22}, B={11,12,13,14}, C= {14, 18,22,24}

D= {13,11,12,14}, E = {-11, 11}, F= {10, 19}, G= {11, -11} and H= {10, 11}

6. Is ∅ = {∅}? why?

7. Which of the sets are equal sets? State the reason.

0, ∅, {0}, {∅}.

Solutions

Students can try to solve the problems on their own. Parents and teachers can encourage the students to do so. If they are having any doubt they can verify the solutions. If you are having any further doubt you can contact us through mail, we will help you to clear your doubt.

Set theory

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