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Logic and Truth Tables
Truth tables are logical devices that predominantly show up in Mathematics,
Computer Science, and Philosophy applications. They are used to determine the
truth or falsity of propositional statements by listing all possible outcomes of the
truth-values for the included propositions.
Proposition - A sentence that makes a claim (can be an assertion or a denial) that
may be either true or false.
Examples – “Roses are beautiful.”
“Did you like the movie?”
Conjunction – an “and” statement. Given two propositions, p and q, “p and q”
forms a conjunction. The conjunction “p and q” is only true if both p and q
are true. The truth table can be set up as follows…
Truth Table for Conjunction “p and q” (p ˄ q)
p q p and q
True True True
True False False
False True False
False False False
Examples – Determine whether the Conjunction is True or False.
a. The capital of Ireland is Dublin and penguins live in Antarctica.
b. A square is a quadrilateral and fish are reptiles.
This is a
Proposition
–
It is a
complete sentence
and
makes a claim. The claim may or may not be true.
This is
NOT
a proposition
–
It is a question and does
not assert or deny anything.
This C
onjunction is
True
because both of
the individual propositions are true.
This Conjunction is
False
because the second
proposition is false.
Fish are not reptiles
.
This symbol can be used
to represent “and”.
