Consider the boolean function F from $2$ boolean variables defined as F$($x$,$ y$)=$ x $+$ y$.$ Task $2.$ Logic Gates and Logical Connectors $[7$ points$]$

XNOR is a common function for logic gates used on electronic chips. $x$ XNOR $y$ can be defined

Task $3.$ Boolean Algebra $[8$ points$]$

Consider the boolean function $F$ from $2$ boolean variables defined as $F(x,y)\frac{?}{b}=ar(x+y).$

Calculate the values of $F$ in a table.

Is $F$ commutative? In other words is $F(x,y)=F(y,x)?$ Justify clearly, basing your

answer on the table you constructed previously.

Is it true that $\frac{?}{\text{b}\text{a}\text{r}}(\frac{?}{\text{b}\text{a}\text{r}}(x+y)+z)\frac{?}{b}=ar(x\frac{+}{b}ar(y+z))?$ Justify clearly.

$1.$ Calculate the values of F in a table.

$2.$ Is F commutative? In other words is F$($x$,$ y$)=$ F$($y$,$ x$)?$ Justify clearly, basing your

answer on the table you constructed previously.

$3.$ Is it true that x $+$ y $+$ z $=$ x $+$ y $+$ z$?$ Justify clearly.