This set of Discrete Mathematics test focuses on “Algebraic Laws on Sets”.

1. Let C and D be two sets then which of the following statements are true?

1) C U D = D U C

2) C ∩ D = D ∩ C

a) Both of the statements

b) Only 1st statement

c) Only 2nd statement

d) None of the statements

View Answer

Explanation: Commutative laws hold good in sets.

2. If set C is {1, 2, 3, 4} and C – D = Φ then set D can be

a) {1, 2, 4, 5}

b) {1, 2, 3}

c) {1, 2, 3, 4, 5}

d) None of the mentioned

View Answer

Explanation: C ∩ D should be equivalent to C for C – D = Φ.

3. Let C and D be two sets then C – D is equivalent to

a) C’ ∩ D

b) C‘∩ D’

c) C ∩ D’

d) None of the mentioned

View Answer

Explanation: Set C-D will be having those elements which are in C but not in D.

4. For two sets C and D the set (C – D) ∩ D will be

a) C

b) D

c) Φ

d) None of the mentioned

View Answer

Explanation: C-D ≡ C ∩ D’, D ∩ D’ ≡ Φ.

5. Which of the following statement regarding sets is false

a) A ∩ A = A

b) A U A = A

c) A – (B ∩ C) = (A – B) U (A –C)

d) (A U B)’ =A’ U B’

View Answer

Explanation: (A U B)’ = A’ ∩ B’.

6. Let C = {1,2,3,4} and D = {1, 2, 3, 4} then which of the following hold not true in this case

a) C – D = D – C

b) C U D = C ∩ D

c) C ∩ D = C – D

d) C – D = Φ

View Answer

Explanation: C ∩ D = {1, 2, 3, 4} ≠ Φ.

7. If C’ U (D ∩ E’) is equivalent to

a) (C ∩ (D U E))’

b) (C ∩( D∩ E’))’

c) (C ∩( D’ U E))’

d) (C U ( D ∩ E’)’

View Answer

Explanation: (C’)’≡ C, (C∩ D)’ ≡ C’ U D’.

8. Let Universal set U is {1, 2, 3, 4, 5, 6, 7, 8} ,(Complement of A) A’ is {2, 5, 6, 7}, A ∩ B is {1, 3, 4} then the set B’ will surely have of which of the element

a) 8

b) 7

c) 1

d) 3

View Answer

Explanation: The set A is {1,3,4,8} and thus surely B does not have 8 in it. Since 8 does not belong to A ∩ B. For other element like 7 we can’t be sure.

9. Let a set be A then A ∩ φ and A U φ are respectively

a) φ, φ

b) φ, A

c) A, φ

d)None of the mentioned

View Answer

Explanation: By Domination Laws on sets.

10. If in sets A, B, C, the set B ∩ C consists of 8 elements, set A ∩ B consists of 7 elements and set C ∩ A consists of 7 elements then the minimum element in set A U B U C will be

a) 8

b) 14

c) 22

d) 15

View Answer

Explanation: For minimum elements set B and C have 8 elements each and all of the elements are same, Also set A should have 7 elements which are already present in B and C. Thus A U B U C ≡ A ≡ B.

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