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