Which of the following is false?

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

Question

(C) For the set of natural numbers $N$ with respect to addition,the operation is commutative $(a+b = b+a)$ and associative $((a+b)+c = a+(b+c))$.For t

Vedclass · Accepted Answer

If $a * b = a^{b}$ for all $a, b \in N$,then $*$ is commutative in $N$.

Vedclass · Answer

(C) For the set of natural numbers $N$ with respect to addition,the operation is commutative $(a+b = b+a)$ and associative $((a+b)+c = a+(b+c))$.For the set of natural numbers $N$ with respect to multiplication,the operation is associative $((a 	imes b) 	imes c = a 	imes (b 	imes c))$.For the operation $a * b = a^{b}$,we check for commutativity: $a * b = a^{b}$ and $b * a = b^{a}$.Since $a^{b} 
eq b^{a}$ for all $a, b \in N$ (e.g.,$2 * 3 = 2^{3} = 8$ while $3 * 2 = 3^{2} = 9$),the operation $*$ is not commutative.Therefore,option $C$ is false.

Similar Questions

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

State whether the following statement is true or false. Justify: For an arbitrary binary operation $^$ on a set $N$,$a \,^ \,a = a$ for all $a \in N$.

Let $P$ be the set of all subsets of a given set $X$. Show that $\cup: P \times P \rightarrow P$ given by $(A, B) \rightarrow A \cup B$ and $\cap: P \times P \rightarrow P$ given by $(A, B) \rightarrow A \cap B$ are binary operations on the set $P$.

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

The binary operation $$ on $R - \{-1\}$ defined by $a b = \frac{a}{b+1}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module