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 $d$.
$$
\begin{array}{l}
2 * 4=2(4)+1=9 \\
(2 * 4) * 2=9 * 2=9(2)+1=19
\end{array}
$$

List the prime number in ascending order: $2,3,5,7,11,13,17,19$.
$$
\begin{array}{l}
b=8 \\
c=\frac{1}{2} \cdot \frac{2}{3} \cdot \frac{3}{4} \cdots \cdots \frac{49}{50}=\frac{1}{50}
\end{array}
$$

Diameter $=20=$ diagonal of the square
Let the side of the square be $x$.
By Pythagoras' Theorem, $2 x^{2}=20^{2}=400$
$$
d=x^{2}=200
$$