Set Theory

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

Click on each question to see answer & solution.

Question No: #31

If `A={1, 2, 3}`, `B = {3, 4}`, `C={4, 5, 6}`, then `(A \times C) \cap (B \times C)` = --
(a) {(1,4), (3,4)}, (b) {(3,4)}, (c) {3,4}, (d) none of these.
Ans: (b) {(3,4)}
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Question No: #32

`(A \cup B \cup C) \cap (A \cap B^c \cap C^c) \cap C^c` equals to the set -
(a) `B \cap C^c`, (b) `A \cap C`, (c) `B^c \cap C^c`, (d) none of these.
Ans: (a) `B \cap C^c`
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Question No: #33

`A`, `B` are `C` three sets and `A \cup B \cup C = S` (`S` = universal set). Then `{(A - B) \cup (B - C) \cup (C - A)}^c` equals to the set --
(a) `A \cup B \cup C`, (b) `A \cup (B \cap C)`, (c) `A \cap B \cap C`, (d) `A \cap (B \cup C)`
Ans: (c) `A \cap B \cap C`
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Question No: #34

If `a\mathbb{N}={ax | x\in\mathbb{N}}`, then find `3\mathbb{N} \cap 7\mathbb{N}`

Question No: #35

If `B\subseteqA`, then prove that `B-A=\phi`
Ans: N.A.
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Question No: #36

Find the H.C.F. of `15,40,105` and L.C.M of `12,15,20` by Set Theory.

Question No: #37

If `A = {x : -1 \lt x \le 5}` and `B = {x : -3 \le x \lt 4}`, then find `A \cap B`

Question No: #38

If `U` be the universal set and `A,B` are two subsets of `U` where `U={1,3,5,7,9,12,15}`, `A={1,5,9,15}`, `B={3,7,9,12,15}`, then find the following sets.
(a) `A^c`, (b) `A\cupB`, (c) `A\capB`, (d) `A-B`, (e) `B-A`, (f) `A^c\cupB^c`, (g) `A^c\capB^c`, (h) `(A\capB)\cup(A-B)`
Ans: (a) `A^c = {3, 7,12}`
(b) `A \cup B = {1, 3, 5, 7, 9, 12, 15}`
(c) `A \cap B = {9, 15}`
(d) `A - B = {1, 5}`
(e) `B - A = {3, 7, 12}`
(f) `A^c \cup B^c = {1, 3, 5, 7, 12}`
(g) `A^c \cap B^c = \phi`
(h) `(A \cap B) \cup (A-B) = {1, 5, 9, 15}`
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Question No: #39

If `A={1,2,3,4}`, `B={3,4,5}`, `C={1,4,5}` then verify the following relations.
(a) `A-(B\cupC)=(A-B)\cap(A-C)` (b) `A\cup(B-C)=(A\cupB)-(A\cupC)`
Ans: (a) Valid, (b) Invalid
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Question No: #40

If `A={1,3}`, `B={3,5}`, `C={5,10}` then verify the following relations.
(a) `A\xx(B\cupC)=(A\xxB)\cup(A\xxC)`, (b) `A\xx(B\capC)=(A\xxB)\cap(A\xxC)`
Ans: (a) Valid, (b) Valid
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