Which of the following is not a group with re | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) set $G$ with a binary operation $*$ is a group if it satisfies closure,associativity,existence of identity,and existence of inverse.For the set of

Vedclass · Accepted Answer

The set of odd integers under addition

Vedclass · Answer

(B) set $G$ with a binary operation $*$ is a group if it satisfies closure,associativity,existence of identity,and existence of inverse.For the set of odd integers under addition,let $a = 1$ and $b = 3$. Then $a + b = 4$,which is an even integer.Since the sum of two odd integers is always even,the set of odd integers is not closed under addition.Furthermore,the identity element for addition is $0$,which is not an odd integer.Therefore,the set of odd integers under addition is not a group.

$^*$	$1$	$2$	$3$	$4$	$5$
$1$	$1$	$1$	$1$	$1$	$1$
$2$	$1$	$2$	$2$	$2$	$2$
$3$	$1$	$2$	$3$	$3$	$3$
$4$	$1$	$2$	$3$	$4$	$4$
$5$	$1$	$2$	$3$	$4$	$5$

Which of the following is not a group with respect to the given operation?

Similar Questions

Show that $*: R \times R \rightarrow R$ given by $(a, b) \rightarrow a+4 b^{2}$ is a binary operation.

In a group $(G, *)$,for some element $a$ of $G$,if $a^{2}=e$,where $e$ is the identity element,then

Let $^$ be a binary operation on the set $Q$ of rational numbers defined as $a b = a + ab$. Is the operation $^*$ commutative and associative?

Let $$ be a binary operation defined on the set of rational numbers $Q$. Determine whether the binary operation defined by $a b = a^{2} + b^{2}$ for all $a, b \in Q$ is commutative.

Vedclass Test Series

Exam Paper Generator

Online Exam Module