A$4.$ In the space provided below, simplify $Y$ using Boolean theorems. List the theorem $($relationships$)$ used in each step of simplification.

Basic relationships:

$($a$)$ A$.0=0$

$($b$)$ A$\mathrm{.}1=$A

$($c$)A+0=A$

$($d$)A+1=1$

$($e$)$ A$.$A$=$A

$($f$)A+A=A$

$($g$)A^{\text{'}}+A=1$

$($h$)A^{\text{'}}*A=0$

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A$6.$ Construct the circuit for the simplified expression and verify the operation of the simplified circuit by setting the binary switches $($A$,$ B and C$)$ to each set of input values in Table $3\mathrm{.}2$ and verify that the outputs observed are same as the corresponding outputs of the original circuit.

Questions $($True of False$)$:

# Question

$(\frac{T}{F})$

$1(A+B+C{)}^{\text{'}}=A^{\text{'}}.B^{\text{'}}.C^{\text{'}}$

$2($A$.$B$.$C$)\text{'}=A^{\text{'}}*B^{\text{'}}*C^{\text{'}}$

$3$

A$.(B^{\text{'}}+B)+C=A+C$

$4$

$A(B+C{)}^{\text{'}}=A{B}^{\text{'}}{C}^{\text{'}}$

$A^{\text{'}}*B^{\text{'}}*C^{\text{'}}=(A+B+C{)}^{\text{'}}$

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