Set Theory

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #1

Which of the given statements is true – (a) subset of an infinite set is an infinite set, (b) the set of even numbers greater than 889 is an infinite set, (c) the set of odd negative numbers greater than -150 is an infinite set, (d) A={`x : x` real number and `0\ltx\le1`} is a finite set.
Ans: (b)
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Question No: #2

If `A = {x : x \in \mathbb{Z}` and `0 \lt x \lt 4}` and `B = {x : x \in \mathbb{Z}` and `3 \le x \le 6}`, then `A \cap B` =-?-
(a) `{2}`, (b) `{3}`, (c) `3`, (d) `\phi`
Ans: (b) `{3}`
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Question No: #3

If `A = {(x,y) : y = 1/x, x\ne0, x \in mathbb{R}}` and `B = {(x,y) : y = -x, x \in mathbb{R}}`, then which of the following is true?-
(a) `A \cap B = A`, (b) `A \cap B = B`, (c) `A \cap B = \phi`, (d) None of these.
Ans: (c) `A \cap B = \phi`
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Question No: #4

Which of the following set is a null set?-
(a) `A= {x : x` is prime number and `31 \lt x \lt 37}`, (b) `B = {x : x` is integer and `0 \lt x \le 1}`, (c) `C = {\phi}`, (d) `D = {x : x+1=1}`
Ans: (a) A set
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Question No: #5

Which of the following set is an infinite set ?
(a) A = {`x : x` is an integer and `-1 \le x\lt 1`}, (b) B = set of even negative integers greater than `-100`, (c) C = set of positive integers less than 100, (d) D = {`x : x` is real and `-1 \le x\lt 1`}
Ans: (d) D = {`x : x` is real and `-1 \le x\lt 1`}
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Question No: #6

If `A = {5k +1 : k \in \mathbb{Z}}` and `B = { x : x \in \mathbb{Z}` and `x+4` is divisible by 5`}`, then which of the following is true?--
(a) `A \subset B`, (b) `B \subset A`, (c) `A = B`, (d) `A \cap B = \phi`
Ans: (c) `A = B`
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Question No: #7

If the number of members of two sets `A` and `B` are 3 and 6 respectively, then minimum number of members in the set `A \cup B` is -
(a) 3, (b) 6, (c) 9, (d) 18
Ans: (b) 6
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Question No: #8

If `A\cupB=A\capB`, then which one is true?

(a) `A\subseteqB` (b) `B\subseteqA` (c) `A=B` (d) None of these
Ans: (c) `A=B`
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Question No: #9

The set `A\cap(A\cupB)^c` equals to -

(a) `A` (b) `A^c` (c) `B^c` (d) `\phi`
Ans: (d) `\phi`
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Question No: #10

If `B \subseteq A`, then `B - A` is -
(a) `B`, (b) `A`, (c) `\phi`, (d) `A^c`
Ans: (c) `\phi`
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