MCQs of Algebraic Structures

Showing 1 to 10 out of 65 Questions
1.
${\mathrm{ℤ}}^{*}=_____?$
 (a) {0,1} (b) {-1,1} (c) {0,-1} (d) {1}
2.
${\mathrm{ℤ}}_{n}=_____?$
 (a) {0,1,2,...,n-1} (b) {0,1,2,...,n} (c) {1,2,...,n-1} (d) {1,2,...,2n}
3.
 (a) (b) (c) (d)
4.
_____ is not a binary operation on the set of natural numbers.
 (a) addition (b) product (c) difference (d) none
5.
 (a) + (b) - (c) * (d) /
6.
 (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 *
7.
then * is said to be _____ on S.
 (a) closed (b) commutative (c) associative (d) distributive
8.
For any set S there exist $\mathrm{e}\in \mathrm{S}$ such that a*e=e*a=a, $\forall \mathrm{a}\in \mathrm{S}$ then e is called _____.
 (a) an unique element (b) an identity element (c) an inverse element (d) a proper element
9.
For any set S there exist $\mathrm{b}\in \mathrm{S}$ such that a*b=e for some $\mathrm{a}\in \mathrm{S}$ 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
10.
then * is said to be _____ on S.
 (a) closed (b) associative (c) distributive (d) commutative
Showing 1 to 10 out of 65 Questions