## Problems on set-III

In this page 'Problems on set-III' we are going to see problems on sub set, power set and number of subsets.

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.

Following problems are based on subset.

1. Fill in the blanks with ⊆ or ⊈ to make each statement true.

(i) {3} --- {0,2,4,6}

(ii) {a} ----- {a,b,c}

(iii) {8, 18} ---- {18, 8}

(iv) {d} ---- {{a,b,c}

2.Let X= {-3, -2,-1, 0, 1, 2} and Y = {x: x is an integer and -3 ≤ x < 2}

(i) Is X a subset of Y? (ii) Is Y a subset of X?

3. Examine whether A={x: x is a positive integer divisible by 3} is a subset of B= { x: x is a multiple of 5, x∈ℕ}

Solutions

Following problems are based on power set and number of power sets.

4. Write down the power sets of the following sets.

(i) A = {x, y}

(ii) X = {a, b, c}

(iii) B= {5, 6, 7, 8}

(iv) C =∅

5. Find the number of subsets and the number of proper subsets of the following sets.

(i) A = { 13, 14, 15, 16, 17, 18}

(ii) B = {a, b, c, d, e, f, g}

(iii) C = { x: x∈W, x∉ℕ}

6.(i)If A= ∅, find n[P(A)]

(ii) If n(A) = 3 find n[P(A)].

(iii) If n[P(A)] =512, find n(A)?

(iv) If n[P(A)]=1024, find n(A)?

7. If n[P(A)] =1, what can you say about the set A?

8. Let A = {x: x is a natural number <11}

B = {x: x is an even number 1 < x <21}

C = {x: x is an integer and 15 ≤ x ≤ 25}

(i) List the elements of A, B, C.

(ii) Find n(A), n(B) and n(C).

(iii) State whether the following are True(T) or False (F)

(a) 7 ∈ B

(b) 16 ∉ A

(c) {15, 20, 25} ⊂ C

(d) {10, 12} ⊂ B

Solutions

Students can try to solve the problems in this page 'Problems on set-III' on their own. Parents and teachers can encourage the students to do so. They can verify their answers with solutions given in this page. If you are having any doubt you can contact us through mail, we will help you to clear your doubt.

Set Theory

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