SG. 1 If $x^{*} y=x y+1$ and $a=(2 * 4) * 2$, find $a$.
SG. 2 If the $b^{\text {th }}$ prime number is $a$, find $b$.
SG. 3 If $c=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right) \cdots\left(1-\frac{1}{50}\right)$, find $c$ in the simplest fractional form.
SG. 4 If $d$ is the area of a square inscribed in a circle of radius 10 , find $d$.