If * is an operation such that for two integers p and q, p * q = p + q – 2, then find:
(a) 6 * 2
(b) (- 2) * (- 3)
(c) (- 2) * (4)
(d) (+ 3) * (- 1)
(a) Given that: p * q = p + q – 2
⇒ 6 * 2 = 6 + 2 – 2 = 6 + 0 = 6
Thus, 6 * 2 = 6.
(b) Given that: p * q = p + q – 2
⇒ (- 2) * (- 3) = (- 2) + (- 3) – 2
= -5 – 2 = -7.
Thus, (- 2) * (- 3) = – 7.
(c) Given that: p * q = p + q – 2
⇒ (- 2) * (4) = (- 2) + (4) – 2 = 2 – 2 = 0.
Thus, (- 2) * (4) = 0.
(d) Given that p*q – p + q – 2
⇒ (+ 3) * (- 1) = (+ 3) + (- 1) – 2 = 2 – 2 = 0
Thus, (+ 3) * (- 1) = 0.