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Given that (a*b = ab + a + b) and that (a ♦ b =…

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