Set Theory

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

Click on each question to see answer & solution.

Question No: #21

For two non-empty `A` and `B`, if `A-B=A`, then which of the following is always true ?-
(a) `A \subset B`, (b) `B \subset A`, (c) `A \cap B = \phi`, (d) `B-A=\phi`
Ans: (c) `A \cap B = \phi`
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Question No: #22

The number of subsets of `\phi` is -
(a) 0, (b) 1, (c) 2, (d) none of these.
Ans: (b) 1
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Question No: #23

Which of the following is true? -
(a) `\phi \in {0}`, (b) `0 \in \phi`, (c) `\phi \subseteq {0}`, (d) `{0} \subseteq \phi`
Ans: (c) `\phi \subseteq {0}`
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Question No: #24

If `A={{1},{2},{1,2}}` then which of the following is true?

(a) `1\inA` (b) `{1}\inA` (c) `{1,2}\subsetA` (d) `\phi\inA`
Ans: (b) `{1}\inA`
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Question No: #25

If `A={2,4,6,8}`, then which of the following is correct -
(a) `{2,4} \in A`, (b) `{2,4} \subseteq A`, (c) `{2,4} \subset A`, (d) `{2,4} \in A^c`
Ans: (c) `{2,4} \subset A`
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Question No: #26

If `B` is a power set of `A`, then which of the following is correct?
(a) `A \supset B`, (b) `B \supset A`, (c) `A \in B`, (d) `A = B`
Ans: (c) `A \in B`
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Question No: #27

A is a non-empty set and P(A) is power set of A. Then number of terms in P{P{P{P(A)}}} is -
(a) 0, (b) 1, (c) 4, (d) 16
Ans: (d) 16
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Question No: #28

Power set of `A={\phi,{\phi}}` is -
(a) `{\phi,{\phi},{{\phi}}}`, (b) `{\phi,{\phi},A}`, (c) `{\phi,{\phi},{{\phi}},A}`, (d) none of these.
Ans: (c) `{\phi,{\phi},{{\phi}},A}`
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Question No: #29

For any set, which is true?

(a) `{1}\in{1,2,3}` (b) `1\notin{1,2,3}` (c) `1\subset{1,2,3}` (d) `{1}\subset{1,2,3}`
Ans: (d) `{1}\subset{1,2,3}`
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Question No: #30

For any three sets `A`, `B`, `C`, if `A= B \cap C` and `B = C \cap A` then -
(a) `A \subset B`, (b) `B \subset A`, (c) `A = B`, (d) `A \subset B^c`
Ans: (c) `A = B`
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