ICSE Class 8 Maths Sets Unit Test Paper

Unit Test Paper

Sets

1. State whether the following statements are True or False.

(i) If A = {x | x = 5n, 5 < n < 10, n ∈ N}, then n(A) = 4

(ii) If n(A) = n(B), set A ↔ set B

(iii) Set A = {x | x ∈ N and x < 3} is a singleton set.

(iv) The number of intelligent students in Class VIII B is a set.

(v) The number of students passing the half-yearly exams in Class VIII B of a school is a set.

(vi) A = {x | x = p³, p < 4, p ∈ N} and {x | x = m², m < 4, m ∈ N} are overlapping sets.

(vii) A = {x | x ∈ W} is a subset of B = {x | x ∈ Z}.

(viii) A = {x | x = 2p, p ∈ N} and B = {x | x = 3p, p ∈ N} are disjoint sets.

(ix) If ξ = {p, q, r, s, t, u, v} and A = {q, u, s, t}, then A' = {p, r, v}

(x) If A = {2, 3, 4}, then P(A) = {{}, {2}, {3}, {4}, {2, 3}, {2, 4}, {3, 4}, {2, 3, 4}}

2. If C is a letter in the word SET, write down all the subsets of C.

3. Write down the complements of all the 8 subsets of set C above.

4. If Q = {x | x = a² + 1, 2 ≤ a ≤ 5, a ∈ N}, what is the power set of Q?

5. If x = {x | x < 20 and x ∈ N},

A = {x | x = 2a, 3 < a < 8, a ∈ N},

B = {x | x = 3b, b < 5, b ∈ N}, and

C = {x | x = c + 1, 5 < c < 15, c ∈ N},

find

(i) n(B)

(ii) n(C)

(iii) A'

(iv) B'

(v) P(B)

6. If A = {x | x ∈ N, 3 < x < 10},

B = {x | x = 4a - 1, a < 5, a ∈ N}, and

C = {x | x = 3a + 2, a < 7, a ∈ N},

confirm

(i) the commutative property of union of sets B and C

(ii) the commutative property of intersection of sets A and C

(iii) the associative property of union of sets A, B, and C

(iv) the associative property of intersection of sets A, B, and C

7. If A = {x | x ∈ W, 4 ≤ x ≤ 12},

B = {x | x = a + 1, a < 8, a ∈ N}, and

C = {x | x = 2n, 1 < n < 7, n ∈ N}, find

(i) A - B

(ii) B - C

(iii) B ∩ C

(iv) A - (B ∩ C)

(v) B - (A ∩ C)

(vi) A - C

(vii) A - (B - C)

(viii) A - (B ∪ C)

8. If ξ = {x | x is a letter of the English alphabet between, but not including d and o},

A = {l, m, n},

B = {e, f, g, h, i, j, k, l}, and

C = {j, k, l, m}, find

(i) A' ∪ B'

(ii) B' ∩ C'

(iii) A ∩ C

(iv) B - (A ∩ C)

(v) (B - A)'

(vi) Is (B - C) ⊆ (B - A)?

(vii) Is A' ∩ B' = ∅?

9. All 26 customers in a restaurant had either drinks, snacks, or dinner. 18 had snacks, out of which 6 had only snacks, 4 had snacks and drinks but not dinner, 2 had drinks and dinner but not snacks, and 3 had snacks and dinner but not drinks. If 14 customers had drinks, find:

(i) how many customers had all three - drinks, snacks as well as dinner

(ii) how many customers had dinner but neither snacks nor drinks

(iii) how many customers had only drinks

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