Each of the following expressions can be simplified as one of the $16$ gates listed in the table above. You can either simplify the expressions below or actually construct their logic tables $($all four combinations of boolean values for A and B$).$ Either way, for each expression below determine which of the $16$ binary $($two input$)$ logic operations is equivalent to the expression. Remember, only use numbers as your solution.The table below was found Here

List of logic gates

$1.0,0,0,0(false)$

$2.0,0,0,1(and)$

$3.0,0,1,0(A$ and not $B)$

$4.0,0,1,1(A)$

$5.0,1,0,0($ notA and $B)$

$6.0,1,0,1(B)$

$7.0,1,1,0(xor)$

$8.0,1,1,1(or)$

$9.1,0,0,0(nor)$

$10.1,0,0,1(xnor)$

$11.1,0,1,0($ not $B)$

$12.1,0,1,1(B$ implies $A)$

$13.1,1,0,0($ not $A)$

$14.1,1,0,1(A$ implies $B)$

$1,1,1,0($ nand $)$

$1,1,1,1($ true$)$

Where the first number is the output for $A=$false,$B=$false, the second number is the output

for $A=$false,$B=t$ rue, the third number is the output for $A=t$ rue, $B=$false, the fourth number

is the output for $A=t$ rue, $B=t$ rue.

number $2$ and not the word "two"$)$

expression. Remember, only use numbers as your solution

$Avv{B}^{{?}^{?}}Bvv{A}^{{?}^{?}}{B}^{{?}^{?}}$AvvB

$(AvvnotA)(B^{{?}^{?}}$notB$)$

$A(notB,$vvnotB$)|$

$(not(AvvB{)}^{{?}^{?}}A)vvB$

$(not(AvvB{)}^{{?}^{?}}A)vvt$

$(notnot(AvvnotB{)}^{{?}^{?}}$notA$)vvvv$

$A^{{?}^{?}}{B}^{{?}^{?}}(BB)$

$(AB{)}^{{?}^{?}}(BA)$