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: Option 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