Discrete Mathematics (3140708) MCQs

MCQs of Algebraic Structures

Showing 1 to 10 out of 65 Questions
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1.
ℤ*=_____?
(a) {0,1}
(b) {-1,1}
(c) {0,-1}
(d) {1}
Answer:

Option (b)

2.
ℤn=_____?
(a) {0,1,2,...,n-1}
(b) {0,1,2,...,n}
(c) {1,2,...,n-1}
(d) {1,2,...,2n}
Answer:

Option (a)

3.
*:A×A→A is said to be binary operation if _____.
(a) a*b∈A, for some a∈A
(b) a*b∈A, for some b∈A
(c) a*b∈A, for some a,b∈A
(d) a*b∈A, for all a,b∈A
Answer:

Option (d)

4.
_____ is not a binary operation on the set of natural numbers.
(a) addition
(b) product
(c) difference
(d) none
Answer:

Option (c)

5.
_____ is not a binary operation on ℤ.
(a) +
(b) -
(c) *
(d) /
Answer:

Option (d)

6.
(S, *) is said to be semigroup if _____.
(a) * is binary operation on S
(b) * is associative on s
(c) both A and B
(d) S has an identity element with respect to *
Answer:

Option (c)

7.
If a*(b*c)=(a*b)*c ∀a,b,c∈S then * is said to be _____ on S.
(a) closed
(b) commutative
(c) associative
(d) distributive
Answer:

Option (c)

8.
For any set S there exist e∈S such that a*e=e*a=a, ∀a∈S then e is called _____.
(a) an unique element
(b) an identity element
(c) an inverse element
(d) a proper element
Answer:

Option (b)

9.
For any set S there exist b∈S such that a*b=e for some a∈S then b is called which element of a? Where, e is an identity element on S.
(a) an inverse
(b) an identity
(c) a unit
(d) a proper
Answer:

Option (a)

10.
For any set S if a*b=b*a, ∀a,b∈S then * is said to be _____ on S.
(a) closed
(b) associative
(c) distributive
(d) commutative
Answer:

Option (d)

Showing 1 to 10 out of 65 Questions
1 2 3 4 5 6