Note: The points listed in each question are for grading purposes only. A score out of $100$ will be posted.

Find the values, if any, of the Boolean variable $x$ that satisfy these equations. $(5$ points each$)$

a$)x*1=0$

b$)x+x=0$

c$)x*1=x$

d$)x*\stackrel{}{x}=1$