Chapter 02 Groups
Chapter 02 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