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(B) On the set of positive integers $Z^{+}$,the operation $*$ is defined by $a * b = a - b$. $A$ binary operation $*$ on a set $S$ is a function $*: S

Vedclass · Accepted Answer

No,it is not a binary operation because $a - b$ is not always in $Z^{+}$.

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(B) On the set of positive integers $Z^{+}$,the operation $*$ is defined by $a * b = a - b$. $A$ binary operation $*$ on a set $S$ is a function $*: S 	imes S 	o S$. For the operation to be binary,for every pair $(a, b) \in Z^{+} 	imes Z^{+}$,the result $a * b$ must belong to $Z^{+}$. Consider the elements $a = 1$ and $b = 2$,where $1, 2 \in Z^{+}$. Then $a * b = 1 * 2 = 1 - 2 = -1$. Since $-1 
otin Z^{+}$,the operation $*$ is not a binary operation on $Z^{+}$.

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

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

Similar Questions

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

For the binary operation $^*$ defined on the set $R - \{-1\}$ by $a ^* b = \frac{a}{b+1}$,determine whether $^*$ is commutative or associative.

Let $A = N \times N$ and $^*$ be the binary operation on $A$ defined by $(a, b) \,^*\, (c, d) = (a + c, b + d)$. Determine whether the operation $^*$ is commutative,associative,and has an identity element.

Let $^*$ be the binary operation on $N$ given by $a \, ^* \, b = \text{L.C.M. of } a \text{ and } b$. Find the identity of $^*$ in $N$.

Let $*$ be a binary operation on the set $Q$ of rational numbers defined as $a * b = \frac{ab}{4}$. Which of the following is true?