Let A = {0, 1, 2, 3, 4, 5, 6}. If a, b in A,a | vedclass

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

Question

(C) The operation $a * b$ is defined as the remainder when $ab$ is divided by $7$,where $a, b \in A$.First,we find the identity element $e \in A$ such

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) The operation $a * b$ is defined as the remainder when $ab$ is divided by $7$,where $a, b \in A$.First,we find the identity element $e \in A$ such that $a * e = a$ for all $a \in A$.This means the remainder of $ae$ divided by $7$ is $a$.For $a \in \{1, 2, 3, 4, 5, 6\}$,$a * 1 = 	ext{remainder of } (a 	imes 1) / 7 = a$.Thus,the identity element $e = 1$.To find the inverse of $2$,we need an element $x \in A$ such that $2 * x = e = 1$.This means the remainder of $(2 	imes x)$ divided by $7$ is $1$.Testing values from $A$:$2 * 1 = 2$$2 * 2 = 4$$2 * 3 = 6$$2 * 4 = 8 \equiv 1 \pmod{7}$Since $2 * 4 = 1$,the inverse of $2$ is $4$.

Let $A = \{0, 1, 2, 3, 4, 5, 6\}$. If $a, b \in A$,and $a * b$ is defined as the remainder when $ab$ is divided by $7$,then find the inverse of $2$ under the operation $*$.

Similar Questions

For each binary operation $^$ defined below,determine whether $^$ is commutative or associative. On $Z^+$,define $a ^* b = 2^{ab}$.

Determine whether or not each of the definitions of $$ given below gives a binary operation. In the event that $$ is not a binary operation,give justification for this. On $Z^{+}$,define $$ by $a b = ab$.

Let $^$ be a binary operation on the set $Q$ of rational numbers defined as $a b = (a - b)^2$. Determine whether the operation is commutative and associative.

In $P(X)$,the power set of a non-empty set $X$,a binary operation $$ is defined by $A B = A \cup B, \forall A, B \in P(X)$. Under $*$,which of the following statements is true?

Let $$ be a binary operation defined on $R$ by $a b = \frac{a+b}{4}$ for all $a, b \in R$. Then the operation $*$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Let $A = \{0, 1, 2, 3, 4, 5, 6\}$. If $a, b \in A$,and $a * b$ is defined as the remainder when $ab$ is divided by $7$,then find the inverse of $2$ under the operation $*$.

Similar Questions

For each binary operation $^*$ defined below,determine whether $^*$ is commutative or associative. On $Z^+$,define $a ^* b = 2^{ab}$.

Determine whether or not each of the definitions of $*$ given below gives a binary operation. In the event that $*$ is not a binary operation,give justification for this. On $Z^{+}$,define $*$ by $a * b = ab$.

Let $^*$ be a binary operation on the set $Q$ of rational numbers defined as $a * b = (a - b)^2$. Determine whether the operation is commutative and associative.

In $P(X)$,the power set of a non-empty set $X$,a binary operation $*$ is defined by $A * B = A \cup B, \forall A, B \in P(X)$. Under $*$,which of the following statements is true?

Let $*$ be a binary operation defined on $R$ by $a * b = \frac{a+b}{4}$ for all $a, b \in R$. Then the operation $*$ is: