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Binary Operations — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSBinary Operations1 Mark
Question
Which of the following is true?
  1. * defined by $\text{a}*\text{b}=\frac{\text{a + b}}2$ is a binary operation on Z.
  2. * defined by $\text{a}*\text{b}=\frac{\text{a + b}}2$ is a binary operation on Q.
  3. All binary commutative operations are associative.
  4. Subtraction is a binary operation on N.
✓

Answer

  1. * 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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