Boolean algebra is based on a set of rules that are derived from a small number of basic assumptions. These assumptions are called axioms. Which of the following logic equations are invalid and not part of the axioms o$1$a:$0\mathrm{.}0=0$

$1$b:$1+1=1$

$2$a:$1\mathrm{.}1=1$

$2$b:$0+0=0$

$3$a:$0\mathrm{.}1=1\mathrm{.}0=1$

$3$b:$1+0=0+1=0$

$4$a:$$ If x$=0,$ then x$=1$

$4$b:$$ If x$=1,$ then x$=0$f Boolean algebra?