Question

If ∆ is an operation on integers such that for integers a and b, a ∆ b = a − b − (− 5). Find the values of

(i) (− 7) ∆ 3 (ii) (− 9) ∆ (− 4) (iii) 2 ∆ 5 (iv) 4 ∆ (− 5)

Answer 1

(i)
∵ a ∆ b = a − b − (− 5)
∴ (− 7) ∆ 3 = (− 7) − 3 − (− 5)
= − 7 − 3 + 5
= − (7 + 3) + 5
= − 10 + 5
= − (10 − 5)
= − 5
(ii)
(− 9) ∆ (− 4) = (− 9) − (− 4) − (− 5)
= − 9 + 4 + 5
= − 9 + 9
= 0

(iii)
2 ∆ 5 = 2 − 5 − (− 5)
= 2 − 5 + 5
= 2
(iv)
4 ∆ (− 5) = 4 − (− 5) − (− 5)
= 4 + 5 + 5
= 14