Set Theory Model Questions Set 2 Practice Questions Answers Test with Solutions & More Shortcuts
Set Theory PRACTICE TEST [2 - EXERCISES]
Set Theory Model Questions Set 1
Set Theory Model Questions Set 2
Question : 6
The set of natural numbers is closed under
I. addition
II. subtraction
III. multiplication
IV. division
Which of the above is/are correct?
a) I, II and III
b) Both I and III
c) Only I
d) Both III and IV
Answer »Answer: (b)
Set of natural numbers,
N = {1, 2, 3, 4, 5, 6, ...
(i) Addition: 2 + 3 = 5 is also an element of N.
(ii) Subtraction: 2 – 3 = –1 ∉ N
(iii) Multiplication: 2 × 3 = 6 ε N
(iv) Division: $3/2$. = 1.5 ∉ N (since, N contains only positive integers)
Therefore, the set of natural numbers is closed under addition and multiplication.
Question : 7
Consider the following in respect of the sets A and B.
I. (A ∩ B) ⊆ A
II. (A ∩ B) ⊆ B
III. A ⊆ (A ∪ B)
Which of the above are correct?
a) I and III
b) II and III
c) I and II
d) I, II and III
Answer »Answer: (d)
From figure,
(A ∩ B) ⊆ A (true)
(A ∩ B) ⊆ B (true)
and A ⊆ (A ∪ B) also (true)
Thus, all three statements are correct.
Shaded region = (A ∪ B).
Question : 8
A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the remainder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A ?
a) Two
b) One
c) No integer
d) Three
Answer »Answer: (b)
LCM of 2, 3, 4, 5, 6 = 60
Number when divided by 2, 3, 4, 5, 6 gives
remainder 1, 2, 3, 4, 5 respectively here 2 – 1 = 1
3 – 2 = 1, 4 – 3, = 1, 5 – 4 = 1, 6 – 5 = 1
So required no. = 60 – 1 = 59
other no. 59 × 2 = 118
i.e. there is one no. below 100.
Question : 9
Which one of the following is a correct statement?
a) Φ = P(Φ)
b) Φ ∉ P (Φ)
c) Φ ε Φ
d) Φ ε P(Φ)
Answer »Answer: (d)
In the given options, the correct statement is Φ ε P(Φ).
Question : 10
Which one of the following is an infinite set?
a) {x : x is a positive integer less than or equal to 1000}
b) {x : x is a natural number less than 1000}
c) {x : x is a whole number less than or equal to 1000}
d) {x : x is an integer and less than 1000}
Answer »Answer: (d)
In a given option only,
{x : x is an integer and less than 1000}
i.e., x ε (– ∞, 1000) is an infinite set.
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Set Theory Model Questions Set 2 Online Quiz
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