A Propositional logic formula analysis tool
Truth tables and expression trees are wonderful tools for
understanding formulas in propositional logic. However, they
are tedious to do by hand. And whenever anything is tedious to
do by hand we should ... have a computer do it for us!
To that end, check out ...
The SI242 Propositional logic
formula analysis tool
ACTIVITY: Use the above tool to explore and discover with a partner
-
What's the easiest way you can find to determine whether two formulas
are equivalent? For example:
- Are a⊕b⇒b∧¬c and (a⇔b)∨¬(b⊕c) equivalent?
- Are a⊕b⇒b∧¬c and (a⇔b)∨¬(b⇒c) equivalent?
-
A binary operator $\small\mbox{ op}$ is said to have the commutative property
if for all operands $a$ and $b$, it holds that
$a {\small\mbox{ op }} b = b {\small\mbox{ op }} a$.
Of our propositional operators
$\wedge,\vee,\Rightarrow,\Leftrightarrow,\oplus$, which are
commutative and which are not? How can you prove
that an operator is commutative? How can you prove
that an operator is not commutative?
-
A binary operator $\small\mbox{op}$ is said to have the associative property
if for all operands $a$, $b$ and $c$, it holds that
$(a {\small\mbox{ op }} b) {\small\mbox{ op }} c = a {\small\mbox{ op }} (b {\small\mbox{ op }} c)$.
Of our propositional operators
$\wedge,\vee,\Rightarrow,\Leftrightarrow,\oplus$, which are
associative and which are not? How can you prove
that an operator is associative? How can you prove
that an operator is not associative?
-
What is the simplest formula you can find that is equivalent
to ite(a,b,c)? ["Simplest" is not precise, so use your own
judgement on what constitutes "simple".]
Use the tool to check that the truth table for your formula
matches that of the ite function!