Discrete Mathematics Multiple Choice Questions on “Subsets”.
1. If a set contains 3 elements then the number of subsets is?
a) 6
b) 3
c) 12
d) 8
Answer: d
Clarification: For elements with n elements the number of subsets are 2n.
2. The set containing all the collection of subsets is known as _________
a) Subset
b) Power set
c) Union set
d) None of the mentioned
Answer: b
Clarification: Power set contains all the subsets as its elements.
3. If a set is empty then number of subsets will be _________
a) 1
b) 2
c) 0
d) 4
Answer: a
Clarification: The set has zero elements so 2o = 1.
4. If the number of subsets of a set are 4 then the number of elements in that sets are _________
a) 1
b) 2
c) 3
d) 4
Answer: b
Clarification: The number of elements be x then x2 = 4 thus x=2.
5. The number of subsets of a set is 5.
a) True
b) False
Answer: b
Clarification: The number of subsets will always be a power of 2.
6. The number of subsets of a set can be odd or even.
a) True
b) False
Answer: a
Clarification: The number of subsets will be odd in case of empty set otherwise even.
7. Let a set be A={1, 2, 3} then the number of subsets containing two elements will be _________
a) 4
b) 3
c) 5
d) 8
Answer: b
Clarification: The subsets will be {1, 2}, {2, 3}, {1, 3}.
8. Let the set be A= {a, b, c, {a,b}} then which of the following is false?
a) {a, b} Є A
b) a Є A
c) {a} Є A
d) b, c ЄA
Answer: c
Clarification: Only elements belongs to a set, {a} is a subset of this set.
9. If A={1, 2, 3, 4}, then the number of the subsets of A that contain the element 2 but not 3, is?
a) 16
b) 4
c) 8
d) 24
Answer: b
Clarification: The subsets would be {1, 2, 4},{1, 2}, {2, 3}, {2}.
10. Let A(1), A(2), A(3),…….., A(100) be 100 sets such that number of elements in A(i)=i+1 and A(1) is subset of A(2), A(2)is subset of A(3),….., A(99) is subset of A(100). The number of elements in union of the all the sets are: n(A(1) U A(2) U A(3) …..U A(100)).
a) 99
b) 100
c) 101
d) 102
Answer: c
Clarification: Since all sets are subsets of A(100) therefore in union only elements of A(100)will come.A(100) contains 101 elements.