MCQs of Algebraic Structures (Discrete Mathematics - 3140708)

Discrete Mathematics (3140708) MCQs

MCQs of Algebraic Structures

Showing 51 to 60 out of 65 Questions

51.

Let

(G, *)

and

(H, ∆)

be two groups. A mapping

g : G \to H

is called a group homomorphism from

(G, *)

(H, ∆)

if for any

a, b \in G

\Rightarrow

_____.

(a)	$g (a * b) = g (a) * g (b)$
(b)	$g (a * b) = g (a) ∆ g (b)$
(c)	$g (a ∆ b) = g (a) ∆ g (b)$
(d)	$g (a ∆ b) = g (a) * g (b)$

52.

If H={0, 3} and G=

(ℤ_{6}, +_{6})

then how many distinct left cosets of H in G?

(a)	1
(b)	2
(c)	3
(d)	4

53.

Let

(ℤ, +)

be a group and

H = 5 ℤ

. Then o(G/H) is _____.

(a)	1
(b)	5
(c)	25
(d)	$\infty$

54.

An algebraic structure

(R, +, \cdot)

is called a ring if the binary operations '+' and '

\cdot

' on S satisfy _____.

(a)	(R, +) is an Abelian group
(b)	(R, $\cdot$ ) is a semigroup
(c)	' $\cdot$ ' is distributive over '+'
(d)	all of these

55.

Which of the following is not a ring?

(a)	$(ℕ, +, \cdot)$
(b)	$(ℤ, +, \cdot)$
(c)	$(ℚ, +, \cdot)$
(d)	$(ℝ, +, \cdot)$

56.

The ring

(S, +, \cdot)

is called a ring with identity if _____.

(a)	$(S, \cdot)$ is commutative
(b)	$(S, \cdot)$ is monoid
(c)	$(S, \cdot)$ semi group
(d)	$(S, \cdot)$ satisfy associative property

57.

If there exists non zero elements

a, b \in (R, +, \cdot)

such that

a \cdot b = 0

then a and b are called _____.

(a)	zeros
(b)	zero elements
(c)	zero divisors
(d)	none of these

58.

A commutative ring with identity

(R, +, \cdot)

is integral domain if it has _____.

(a)	Unity
(b)	Zeros
(c)	zero divisors
(d)	no zero divisor

59.

Which of the following is not an integral domain?

(a)	$(ℕ, +, \cdot)$
(b)	$(ℤ, +, \cdot)$
(c)	$(ℚ, +, \cdot)$
(d)	$(ℝ, +, \cdot)$

60.

An algebraic structure

(F, +, \cdot)

is called field if _____.

(a)	$(F, +)$ is an Abelian group
(b)	$(F^{*}, \cdot)$ is an Abelian group
(c)	$\cdot$ is distributive over +
(d)	all of these

Showing 51 to 60 out of 65 Questions