Which of the following is true? 1. * defined by a*b= a + b 2 is a… - Vidyadip

Question

Which of the following is true?

* 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.
All binary commutative operations are associative.
Subtraction is a binary operation on N.

✓

Answer

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

Solution:

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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