Solution to Construct a truth table for each of these compound propositions. [6 marks] a) p ⊕ … - Sikademy
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Archangel Macsika

Construct a truth table for each of these compound propositions. [6 marks] a) p ⊕ p b) p ⊕¬p c) p ⊕¬q d) ¬p ⊕¬q e) (p ⊕ q) ∨ (p ⊕¬q) f ) (p ⊕ q) ∧ (p ⊕¬q)

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Let us construct the trush table for the following compound propositions:

a) p ⊕ p


\begin{array}{||c||c|c|c|c|c||} \hline\hline p & p ⊕p \\ \hline\hline 0 & 0 \\ \hline 1 & 0\\ \hline\hline \end{array}


b) p ⊕\neg p


\begin{array}{||c||c|c|c|c|c||} \hline\hline p & \neg p & p ⊕ \neg p \\ \hline\hline 0 & 1 & 1 \\ \hline 1 & 0 & 1\\ \hline\hline \end{array}


c) p ⊕\neg q


\begin{array}{||c|c||c|c|c|c||} \hline\hline p & q & \neg 𝑞 & p ⊕\neg q \\ \hline\hline 0 & 0 & 1 & 1 \\ \hline 0 & 1 & 0 & 0\\ \hline 1 & 0 & 1 & 0\\ \hline 1 & 1 & 0 & 1\\ \hline\hline \end{array}


d) \neg p ⊕\neg q


\begin{array}{||c|c||c|c|c|c||} \hline\hline p & q & \neg 𝑝& \neg q & \neg p ⊕\neg q\\ \hline\hline 0 & 0 & 1 & 1 & 0\\ \hline 0 & 1 & 1 & 0 & 1\\ \hline 1 & 0 & 0 & 1 & 1\\ \hline 1 & 1 & 0 & 0 & 0\\ \hline\hline \end{array}


e) (p ⊕ q) ∨ (p ⊕\neg q)


\begin{array}{||c|c||c|c|c|c||} \hline\hline p & q & \neg q & p ⊕\neg q & p ⊕ q & (p ⊕ q) ∨ (p ⊕\neg q) \\ \hline\hline 0 & 0 & 1 & 1 & 0 & 1\\ \hline 0 & 1 & 0 & 0 & 1 & 1\\ \hline 1 & 0 & 1 & 0 & 1 & 1\\ \hline 1 & 1 & 0 & 1 & 0 &1\\ \hline\hline \end{array}


f ) (p ⊕ q) \land (p ⊕\neg q)


\begin{array}{||c|c||c|c|c|c||} \hline\hline p & q & \neg q & p ⊕\neg q & p ⊕ q & (p ⊕ q) \land (p ⊕\neg q) \\ \hline\hline 0 & 0 & 1 & 1 & 0 & 0\\ \hline 0 & 1 & 0 & 0 & 1 & 0\\ \hline 1 & 0 & 1 & 0 & 1 & 0\\ \hline 1 & 1 & 0 & 1 & 0 &0\\ \hline\hline \end{array}

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