Chapter 2 SETS, FUNCTIONS AND GROUPS
2) Let A = {a, b, c, d} B = {b, c, d} then A Ç B =
A) {b, c, d}
B) {a, b, c}
C) {a, b, c, d}
D) {a, c, d}
Answer: A
4) Let A = (1, 2, 3, 4, 5 …..}, B = {2, 4, 6,
8 ….}
The
AÈB is
A) {1, 2, 3}
B) {1, 2, 3, 4, 5, …..}
C) {2, 4, 6, 8, …..}
D) {6, 7, 8, 9}
Answer: B
5) L È M = LÇM then L is equal to
A) M
B) L
C) f
D) M¢
Answer: A
6) Which of the following sets has only one subset.
A) {Y, Z}
B) {Y}
C) {0}
D) { }
Answer: D
7) A Í B then
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A)
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A Ç B
= A
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B)
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A Ç B¢ =
A
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C)
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A – B = A
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D)
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A – B = B
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Answer:
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A
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9) Total number of subsets that can be formed from the
set
{x, y, z} is
A) 1
B) 2
C) 5 D) 8
Answer: D
11) Let A and B be any none empty sets then
AÈ(AÇB) is
A) B Ç A
B) A
C) B
D) A È B
Answer: B
12) Let A, B, C be any sets. Let A È B = A È C and A Ç B = A Ç C, then B set is equal to
A) A È B
B) A Ç B
C) A
D) C
Answer: D
13) If S contains n elements then power set of S, P (s)
contains elements. Which are?
A) 2n
B) 4n
C) 5n D) 6n
Answer: A
14) A set is a collection of objects which are
A) well defined
B) well defined and distinct
C) identical
D) not defined
Answer: B
15) The power set of a set S containing six numbers is the
set whose elements are
A) three subsets of S
B) two subsets of S
C) five subsets of S
D) all possible subsets of S
Answer: D
16) A is a subset of B if
A) Every element of A Î B
B) Some element of A Î B
C) Every element of A Ï B
D) Every element of B Î A
Answer: A
17) The complement of set A relative to universal set U is
the
set
A) {x/xÎU and x ÎA}
B) {x/xÏU and xÏA}
C) {x/xÏU and x ÎA}
D) {x/xÎU and x Ï A}
Answer: D
18) If A \ B = A then
A) AÇB = A
B) AÇB = A¢
C) AÇB = B
D) AÇB = f
Answer: D
19) If B – A = B then
A) AÇB = f
B) AÇB = A
C) AÇB ¹ f
D) AÇB = B
Answer: A
20) The union of the sets A and B is defined as
A) A È B = {x/xÎA or xÎB} B) A È B = {x/xÏA or xÎB} C) A È B = {x/xÏA or xÏB}
D) A È B = {x/xÎA or xÏB}
Answer: A
21) If Q, R are any sets then Q – R =
A) Q – (QÇR)
B) Q Ç (Q – R)
C) Q + (Q Ç R)
D) Q – (Q È R)
Answer: A
22) If A and B are any two sets and A¢ B¢ are Their
compliments relative to the
universal set U, the (AÈB)¢ =
A) A¢ÈB¢
B) AÈB
C) A¢ÇB¢
D) AÇB
Answer: C
23) Difference between two sets A\B is defined as
A) {x/x Î A L x Î B} B) {x/x Î A L x Ï B} C) {x/x Ï A L x Î B}
D) {x/x Ï A L x Ï B}
Answer: B
24) For union Associative Law is
A) (AÈB) ÈC = AÈ(BÈC) B) (AÈB) ÈC = AÇ(BÇC)
C) (AÇB) ÈC = AÈ(BÈC)
D) (AÈB) ÈC = A - (B - C)
Answer: A
25) The set of odd numbers between 1 and 9 is
A) {1, 3, 5, 7}
B) {3, 5, 7, 9}
C) {1, 3, 5, 7, 9}
D) {3, 5, 7}
Answer: D
26) The set of rational numbers between 5 and 9 is
A) Finite
B) Infinite
C) {5, 6, 7, 8, 9}
D) {6, 7, 8}
Answer: B
27) If x is a set having 6 elements then the numbers in
P(x) is:
A) 62
B) 6
C) 6(2)
D) 26
Answer: D
28) If B Í A then A¢ is subset of A) A
B) B
C) B¢
D) A È B
Answer: C
29) The set A Ç (A È B) = A) A
B) B
C) A È B
D) None of these
Answer: A
30) The set A È (A Ç B) =
A) B
B) A
C) A È B
D) None of these
Answer: B
31) If A and B are any two sets and A¢, B¢ are their complements relative to the universal set U, then
A) Ç B)¢ =
A) A¢ È B¢
B) A¢ Ç B¢
C) A¢ È B
D) A Ç B¢
Answer: A
32) If A Í U then A¢ relative to U is equal to
A) A – B
B) B – A
C) U – A D) A
– U
Answer: C
37) Well defined collection of distinct objects is called
a
__________
A) a function
B) a set
C) a real number
D) none
Answer: B
38) A diagram which represents a set is called _______
diagram.
A) Venn’s
B) Argand
C) Plane
D) None
Answer: A
39) If a set A is the subset of B & A ≠ B, then A
_______ of B.
A) Proper subset
B) Improper subset
C) None D)
None
Answer: A
40) Every set is the ________ of itself.
A) proper subset
B) improper subset
C) super set
D) none
Answer: B
41) The set of real Nos. (points) belonging to interval
(a, b) is __________
A) finite set
B) empty set
C) singleton set
D) infinite set
Answer: D
42) The power set of an empty set is _________
A) null set
B) singleton set
C) super set
D) none
Answer: B
43) X / = ________
A) A
B) A /
C) – -
D) X
Answer: C
44) Two set A & B are called overlapping if A∩B
=
________
A) AÍB, BÍA
B) AÍB
C) AÍB, BÍA
D) None
Answer: D
45) Which one is always true.
A) AÍB
B) AÇBÍB
C) BÍA
D) none
Answer: B
46) Every recurring non terminating decimal represents
A) Q
B) Q/
C) R
D) none
Answer: A
47) If X & Y are two sets & n (X) = 18, n (Y) =
24, n(XUY)
= 40 then n(X I Y)
= ________
A) 3
B) 4
C) 6
D) 2
E) 1
Answer: C
48) A real number is always
A) a natural no
B) positive integer
C) Rational number
D) complex number
Answer: D
Groups
1) The set N of natural numbers is closed with respect to
A) Addition
B) Multiplication
C) Both A & B
D) Subtraction
Answer: C
2) The set Z of integers is closed with respect to
A) Addition
B) Multiplication
C) Subtraction
D) A, B and C are correct
Answer: D
3) The set R – {0} of real numbers is closed with respect
to
A) Addition
B) Multiplication
C) Division
D) A,B & C are correct
Answer: D
4) In the set S = {0, 1} the binary operation defined
is
A) – B) +
C) ´
D) ¸
Answer: C
5) The set S = {- 1, 1, - i, i} is a group with respect
to the binary operation
A) ¸
B) ´
C) +
D) –
Answer: B
6) The set S = {1, w, w2} is a
group with respect to the binary operation
A) ´
B) ¸
C) +
D) –
Answer: A
7) If set is a group with respect to addition then the
number of identity elements in S is
A) Unique
B) Two
C) Three
D) None
Answer: A
8) If set S is a group with respect to addition then each
element of S has _____ inverse.
A) Unique
B) Two
C) Three
D) None
Answer: A
9) R – {0} is a group w.r.t the binary operation
A) +
B) ´
C) ¸
D) –
Answer: B
10) Q – {0} is a group w.r.t the binary operation
A) +
B) ´
C) ¸
D) –
Answer: B
11) R is a group w.r.t the binary operation.
A) +
B) ´
C) ¸
D) –
Answer: A
12) Q is a group w.r.t the binary operation.
A) +
B) ´
C) ¸
D) –
Answer: A
13) S = {1, - 1} is a group w.r.t the binary operation.
A) +
B) ´
C) -
D) none of these
Answer: B
14) S = {0} is a trivial group under
A) +
B) ´
C) ¸
D) –
Answer: A
15) S = {1} is trivial group under
A) +
B) ´
C) –
D) division
Answer: B
16) A non empty set S which is closed with a binary
operation
‘*’ is called group if
A) The binary operation is associative
B) There exists identity element with respect to the
binary operation.
C) There exist a unique inverse of each element of S with
respect to the binary operation. D) All A, B & C hold.
Answer: D
17) In a proposition if p→ q
then q → p is called
A) inverse of p→ q
B) converse of p→ q
C) contrapasitive p→ q
D) none
Ans: B
18) Truth table containing all false values is called
A) Tautology
B) Selfcontridiction
C) Equivallent
D) None Ans: B
19) Truth table containing all true values is called
A) Tautology
B) Selfcontridiction
C) Equivallent
D) None
Ans: A
20) In a proposition if p→ q then contrapasitive of this
proposition is denoted by
A) q → p
B) ~ q → p
C) ~ q → ~ p
D) None
Ans: C
21) In a proposition if p→ q then inverse of this
proposition is denoted by
A) q → p
B) ~ q → p
C) ~ p → ~ q
D) None
Ans : C
22) In a proposition if p→ q then converse of this
proposition is denoted by
A) q → p
B) ~ q → p
C) ~ q → ~ p
D) None
Ans: A
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