Given that \(ab = ab + a + b\) and that \(a ♦ b = a + b = 1\). Find an expression (not involving or ♦) for (ab) ♦ (ac) if a, b, c, are real numbers and the operations on the right are ordinary addition and multiplication of numbers

A.

ac + ab + bc + b + c + 1

B.

ac + ab + a + c + 2

C.

ab + ac + a + b + 1

D.

ac + bc + ab + b + c + 2

E.

ab + ac + 2a + b + c + 1

Correct answer is E

Soln. a*b = ab + a + b,

a ♦ b = a + b + 1

a*c = ac + a + c

(a*b) ♦ (a*c) = (ab + a + b + ac + a + c + 1)

= ab + ac + 2a + b + c + 1

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Given that \(a*b = ab + a + b\) and that \(a ♦ b = a + b = 1\). Find an expression (not involving * or ♦) for (a*b) ♦ (a*c) if a, b, c, are real numbers and the operations on the right are ordinary addition and multiplication of numbers