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
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #32697)