Truth Table
Mathlet
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This mathlet creates the truth table for a logical compound
proposition. Type one in (followed by the ENTER key) using the following
syntax:
Mathlet Symbol 
Mathematics Symbol 
Meaning 
! 

not 
& 

and 
 

or 
> 

implies 
<> 

if and only if 
 

exclusive or 
p 
p 
truth variable 
T 
T 
true 
F 
F 
false 
For a truth variable, any lowercase letter in the ranges ae, gs, uz
(i.e. omitting f and t which are reserved for false and true) may be used. The
negation operator, !, is applied before all others, which are are evaluated
lefttoright. Parentheses, ( ), and brackets, [ ], may be used to enforce a
different evaluation order.
E.g.
p > q
p & (q  r)
[(p > q) & (q > r)] > (p > r)
are all syntactically correct.
To Do
The yellow monitor next to an exercise suggests that you should
solve it using the mathlet and a yellow pencil indicates that pencilandpaper computation
might be necessary.
1. Get familiar with the mathlet by generating the truth tables for the
elementary propositions
and check to see that they're correct!
2. Show that p
q
is logically equivalent to
p
q by creating their truth tables.
3. The converse of p
q is q
p and the
contrapositive of p
q is
q
p. Show that the
converse is
not logically equivalent to the contrapositive by
creating their truth tables.
4. Show that the contrapositive of p
q
is
logically equivalent to p
q by creating their truth tables.
5. Prove the distributive law, p
(q
r) is logically
equivalent to (p
q)
(p
r),
by creating two truth tables.
6. Translate the following sentence into a logical proposition using
three logic variables.
You can connect to the Internet from your dorm room only
if you are a CS major or you have not defaulted on your tuition
payments.
Then use Truth Table to create the truth table for this
proposition. Under what circumstances can a student
not connect to
the Internet from her dorm room? Use the truth table to back up your
assertion. If you are a CS major and have defaulted on your tuition payments,
can you connect? Again, use the truth table to justify your conclusion.
7. Create a logical proposition s in two propositional variables
p and q, with the following truth
table. Use only
,
, and
in your proposition.
p 
q 
s 
T 
T 
F 
T 
F 
T 
F 
T 
F 
F 
F 
T 
Now do the same thing for three propositional variables, p, q, and r.
p 
q 
r 
s 
T 
T 
T 
T 
T 
T 
F 
F 
T 
F 
T 
F 
T 
F 
F 
T 
F 
T 
T 
F 
F 
T 
F 
T 
F 
F 
T 
F 
F 
F 
F 
T 
Informally describe an algorithm to do this for an arbitrary
truth table with n propositional variables.