Question

(iii) the correct pair from the following pairs relations ( where a and rational numbers and a≠0, b ≠ 0) is (a) a+b=b+a, a-b=b-a​

Answer 1

we have to choose the correct pair from the following pairs relation (where a and b are rational number and a ≠ 0 , b ≠ 0)

(a) a + b = b + a

(b) a - b = b - a

Answer : option (a) a + b = b + a

explanation : cumulative laws : it says when we swap the numbers over and still we get the same answer.

for example, 1 + 2 + 3 = 3 + 2 + 1

LHS = 1 + 2 + 3 = 6

RHS = 3 + 2 + 1 = 6

LHS = RHS

hence, 1 + 2 + 3 = 3 + 2 + 1

similarly, 4 × 6 = 6 × 4

LHS = 4 × 6 = 24

RHS = 6 × 4 = 24

hence, 4 × 6 = 6 × 4

but if we see it in subtraction,

3 - 4 = -1

4 - 3 = 1

3 - 4 ≠ 4 - 3

LHS ≠ RHS

hence, substraction doesn't follow cumulative laws.

so a - b ≠ b - a for all rational numbers of a and b except a ≠ 0 and b ≠ 0.

Therefore the correct pair is option (a) a + b = b + a