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
jamb 1978mathematics

The correct answer is E. ab + ac + 2a + b + c + 1

Given that \(a*b = ab + a + b\) and \(a ♦ b = a + b - 1\), we want to find an expression for \((a*b) ♦ (a*c)\).

First, we can substitute the given expressions into \((a*b) ♦ (a*c)\) to get \((ab + a + b) ♦ (ac + a + c)\).

Then, using the definition of the operation ♦, we can simplify this to \((ab + a + b) + (ac + a + c) - 1\).

Finally, rearranging the terms gives us ab + ac + 2a + b + c.

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