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$A, S, M$ and $D$ are functions of $x$ and $y$, and they are defined as follows.

  • $A(x, y) = x + y$
  • $M(x, y) = xy$
  • $S(x,y)= x-y$
  • $D(x,y)= x/y, y\neq 0$

What is the value of $M(M(A(M(x, y), S(y, x)), x), A(y, x))$ for $x = 2, y = 3$?

  1. $60$
  2. $140$
  3. $25$
  4. $70$
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Given that,

  • $A(x,y)=x+y$
  • $M(x,y)=xy$
  • $S(x,y)=x−y$
  • $D(x,y)=x/y;y\ne0$

Now, the value of $M(M(A(M(x,y),S(y,x)),x),A(y,x))$ for $x=2,y=3:$

$\Rightarrow M(M(A(M(2,3),S(3,2)),2),A(3,2))$

$\Rightarrow M(M(A(6,1),2),5)$

$\Rightarrow M(M(7,2),5)$

$\Rightarrow M(14,5)$

$\Rightarrow 70$

Correct Answer $:\text{D}$

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