Discrete Mathematics test on “Algebraic Laws on Sets”.
1. Let C and D be two sets then which of the following statements are true?
i) C U D = D U C ii) C ∩ D = D ∩ C
a) Both of the statements
b) Only i statement
c) Only ii statement
d) None of the statements
Answer: a
Clarification: 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
Answer: c
Clarification: 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
Answer: c
Clarification: 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
Answer: c
Clarification: 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’
Answer: d
Clarification: (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
Answer: c
Clarification: 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’)’
Answer: c
Clarification: (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
Answer: a
Clarification: 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 __________
a) φ, φ
b) φ, A
c) A, φ
d)None of the mentioned
Answer: b
Clarification: 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
Answer: a
Clarification: 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.