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
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: E
Explanation
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
