2 SETS, FUNCTIONS AND GROUPS solved

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

A)	A Ç B = A
B)	A Ç B¢ = A
C)	A – B = A
D)	A – B = B
Answer:	A

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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Tuesday, 6 December 2016

2 SETS, FUNCTIONS AND GROUPS solved

Chapter 2 SETS, FUNCTIONS AND GROUPS

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