JaynesProbabilityTheory/chapter1.html at master · MaksimIM/JaynesProbabilityTheory · GitHub

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<h1 id="plausible-reasoning">Plausible Reasoning</h1>
<p><span class="math inline">\(\leftarrow\)</span> <a href="./index.html">Back to Chapters</a></p>
<h2 id="proof-of-1.13">Proof of 1.13</h2>
<p>if <span class="math inline">\(\overline{B} = AD\)</span> then <span class="math inline">\(A\overline{B}=\overline{B}\)</span>:</p>
<p><span class="math inline">\(\overline{B} = AD\)</span></p>
<p><span class="math inline">\(A\overline{B} = AAD\)</span></p>
<p><span class="math inline">\(A\overline{B} = AD\)</span></p>
<p><span class="math inline">\(A\overline{B} = \overline{B}\)</span></p>
<p><span class="math inline">\(\square\)</span></p>
<p>if <span class="math inline">\(\overline{B} = AD\)</span> then <span class="math inline">\(B\overline{A}=\overline{A}\)</span>:</p>
<p><span class="math inline">\(\overline{B} = AD\)</span></p>
<p><span class="math inline">\(A+\overline{B} = A+AD\)</span></p>
<p><span class="math inline">\(A+\overline{B} = A\)</span> using <a href="https://proofwiki.org/wiki/Absorption_Laws_(Boolean_Algebras)">absorption laws</a>, which can be proved with a truth table</p>
<p><span class="math inline">\(\overline{A}B = \overline{A}\)</span></p>
<p><span class="math inline">\(\square\)</span></p>
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