in Logical Reasoning edited by
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Consider the following operators defined below

[email protected]$: gives the positive difference of $x$ and $y.$

$x\$y$: gives the sum of squares of $x$ and $y.$

$x₤y$: gives the positive difference of the squares of $x$ and $y.$

$x\&y$:gives the product of $x$ and $y.$

Also, $x,y\:\in\:R\:\text{and}\:x\neq y$. The other standard algebraic operations are unchanged.

Given that [email protected]=x-y$, then find $(x\$y)+(x₤y)$.

  1. $2x^2$
  2. $2y^2$
  3. $2(x^2+y^2)$
  4. Cannot be determined
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