Which of the following is true? - Vidyadip

MCQ

Which of the following is true?

A
$*$ defined by $\text{a}*\text{b}=\frac{\text{a + b}}2$ is a binary operation on $Z.$
✓
$*$ defined by $\text{a}*\text{b}=\frac{\text{a + b}}2$ is a binary operation on $Q.$
C
All binary commutative operations are associative.
D
Subtraction is a binary operation on $N.$

✓

Answer

Correct option: B.

$*$ defined by $\text{a}*\text{b}=\frac{\text{a + b}}2$ is a binary operation on $Q.$

For option $a$, if we take $3$ and $2$ then
$3*2=\frac{5}2\in\text{Z}$.
So, option $a$ is not true.
For option $b$, if we take any two numbers $a$ and $b$
then $\frac{\text{a + b}}2$ belongs to $Q$ for $\text{a, b}\in\text{Q}$.
So, option $b$ is correct.
For option $d$, if we take $2, 3$ then $2-3=-1\in\text{N}$.
So, option $d$ is not true.
Option $c$ is not true.

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