If ∆ is an operation on integers such that a ∆ b = −a + b − (−2) for all integers a, b. Find the value of

(i) 4 ∆ 3
(ii) (−2) ∆ (−3)
(iii) 6 ∆ (−5)
(iv) (−5) ∆ 6

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Solution

(i) −4 + 3 − (−2)
= −4 + (3 + 2)
= −4 + 5
= 1

(ii) −(−2) + (−3) − (−2)
= (2 − 3) + 2
= −1 + 2
= 1

(iii) −6 + (−5) − (−2)
= −6 + (−5 + 2)
= −6 − 3
= −9

(iv) −(−5) + 6 − (−2)
= 5 + (6 + 2)
= 5 + 8
= 13

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If ∆ is an operation on integers such that a ∆ b = −a + b − (−2) for all integers a, b. Find the value of (i) 4 ∆ 3 (ii) (−2) ∆ (−3) (iii) 6 ∆ (−5) (iv) (−5) ∆ 6

(i) −4 + 3 − (−2) = −4 + (3 + 2) = −4 + 5 = 1 (ii) −(−2) + (−3) − (−2) = (2 − 3) + 2 = −1 + 2 = 1 (iii) −6 + (−5) − (−2) = −6 + (−5 + 2) = −6 − 3 = −9 (iv) −(−5) + 6 − (−2) = 5 + (6 + 2) = 5 + 8 = 13

If ∆ is an operation on integers such that a ∆ b = −a + b − (−2) for all integers a, b. Find the value of

(i) 4 ∆ 3
(ii) (−2) ∆ (−3)
(iii) 6 ∆ (−5)
(iv) (−5) ∆ 6

(i) −4 + 3 − (−2)
= −4 + (3 + 2)
= −4 + 5
= 1

(ii) −(−2) + (−3) − (−2)
= (2 − 3) + 2
= −1 + 2
= 1

(iii) −6 + (−5) − (−2)
= −6 + (−5 + 2)
= −6 − 3
= −9

(iv) −(−5) + 6 − (−2)
= 5 + (6 + 2)
= 5 + 8
= 13