Question

If a and b are two whole numbers then commutative law is applicable to subtraction if and only if
(a) a = b
(b) a \[\ne \] b
(c) a > b
(d) a < b

Answer 1

Hint: To solve this question we can either separately consider all four points and see which one is wrong or we can directly use the law of commutativity of subtraction to get the answer.
The law of commutativity is,
a + b = b + a or a – b = b – a, where a & b are two numbers.

Complete step-by-step answer:
To solve this question we will first of all see what is commutative law for addition. Two numbers p and q hold commutative law of addition is,
p + q = q + p
Similarly, we can have a commutative law of subtraction. Two numbers p and q said to hole commutative law of subtraction is,
p – q = q – p
Given a and b are two whole numbers.
We have to check when does commutative law of subtraction holds in a and b,
When the law holds we have,
\[\Rightarrow \] a – b = b – a
\[\Rightarrow \] Taking a on one side and b on other side of equation we get,
\[\Rightarrow \] a + a = b + b
\[\Rightarrow \] 2a = 2b
Cancelling 2 from both sides we have,
\[\Rightarrow \] a = b
Hence commutative law holds in subtraction if and only if,
So, the correct answer is “Option A”.

Note: We can check how option b, c and d are wrong.
Consider two numbers a and b such that a \[\ne \] b.
Let a = 4, b = 5.
Then, a – b = 4 – 5 = -1
And b – a = 5 – 4 = 1
Clearly, a – b \[\ne \] b – a, option (b) is incorrect.
Similarly, we can show all other options to be incorrect.
For option (c), consider a > b, Let a = 9, b = 7.
Then a – b = 9 – 7 = 2
And b – a = 7 – 9 = -2
Again a – b \[\ne \] b – a. So option (c) is wrong.
Again consider option (d), a < b.
Let a = 3, b = 7.
Then a – b = 3 – 7 = -4.
And b – a = 7 – 3 = 4.
Clearly, a – b \[\ne \] b – a option (d) is wrong.
So, all options are wrong.