Question

Let * be defined on R by (a * b) = a + b + ab – 7. Is * binary on R? If so, find 3 * `((-7)/15)`

Answer 1

(a * b) = a + b + ab – 7 ∀ a, b ∈ R

If a ∈ R, b ∈ R then ab ∈ R

∴ (a * b) = a + b + ab – 7 ∈ R

For example,

Let 1, 2 ∈ R

(1 * 2) = 1 + 2 + (1)(2) – 7

= – 2 ∈ R

∴ * is a binary operation on R

Now 3 * `(- 7/15)`

= `3 + (- 7/15) + 3(- 7/15) - 7`

= `3 - 7/15 - 21/15 - 7`

= `- 88/15`