$\begingroup$Could someone show me the truth table for this proposition? I think I have the last two down, but I'm not sure what the symbol in the following one is: $$p\oplus (p\wedge q)$$
$\endgroup$12 Answers
$\begingroup$The first symbol that appears in called "exclusive OR" or also known as XOR
XOR will evaluate to false when both values are True, or both values are false.
$$ \begin{array}{cc|c} p & q & p \oplus q \\ \hline T & T & F \\ T & F & T \\ F & T & T \\ F & F & F \end{array} $$
$\endgroup$$\begingroup$$p\oplus t$ is true only when exactly one of $p$ and $q$ is true, knowing this we construct the table in the following way:
$$ \begin{matrix} p & q & p\wedge q & p\oplus (p\wedge q) \\ T & T & T & F \\ T & F & F & T \\ F & T & F & F \\ F & F & F & F \\ \end{matrix} $$
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