Number of binary operations on the set {a, b} | vedclass

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

Question

(C) binary operation $^*$ on a set $S$ is a function from $S 	imes S$ to $S$.Here,the set is $S = \{a, b\}$,so $S 	imes S = \{(a, a), (a, b), (b, a)

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(C) binary operation $^*$ on a set $S$ is a function from $S 	imes S$ to $S$.Here,the set is $S = \{a, b\}$,so $S 	imes S = \{(a, a), (a, b), (b, a), (b, b)\}$.The number of elements in $S 	imes S$ is $n(S 	imes S) = 2 	imes 2 = 4$.The number of elements in the codomain $S$ is $n(S) = 2$.The total number of functions from $S 	imes S$ to $S$ is given by $(n(S))^{n(S 	imes S)} = 2^4$.Calculating this,we get $2^4 = 16$.Thus,the total number of binary operations on the set $\{a, b\}$ is $16$.The correct answer is $C$.

Number of binary operations on the set $\{a, b\}$ are

Similar Questions

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 $a b = |a - b|$.

Show that $+: R \times R \rightarrow R$ and $\times: R \times R \rightarrow R$ are commutative binary operations,but $-: R \times R \rightarrow R$ and $\div: R_* \times R_* \rightarrow R_*$ are not commutative.

Which of the following statements is false?

Consider a binary operation $$ on $N$ defined as $a b = a^{3} + b^{3}$. Choose the correct answer.

Show that the $\vee: R \times R \rightarrow R$ given by $(a, b) \rightarrow \max\{a, b\}$ and the $\wedge: R \times R \rightarrow R$ given by $(a, b) \rightarrow \min\{a, b\}$ are binary operations.

Vedclass Test Series

Exam Paper Generator

Online Exam Module