Plausible Reasoning

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Proof of 1.13

if \(\overline{B} = AD\) then \(A\overline{B}=\overline{B}\):

\(\overline{B} = AD\)

\(A\overline{B} = AAD\)

\(A\overline{B} = AD\)

\(A\overline{B} = \overline{B}\)

\(\square\)

if \(\overline{B} = AD\) then \(B\overline{A}=\overline{A}\):

\(\overline{B} = AD\)

\(A+\overline{B} = A+AD\)

\(A+\overline{B} = A\) using absorption laws, which can be proved with a truth table

\(\overline{A}B = \overline{A}\)

\(\square\)