chapter1.md

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

$\overline{A}B = \overline{A}$

$\square$