# Constructing a truth table

#### darleneporter

##### New member
Can someone please help me, i am a little off with this question.

Construct a truth table for the statement.
s v (s ^ ~s)
&
(s ^ w)^(~w v t)

now, i am lost. also, could you also check the ones i have done below to see if i am on the right track:

Construct a truth table for the statement.
(p ^ ~q)^ s

p q s (p ^ ~q)^ s
t t t f
t t f f
t f t f
t f f f
f t t f
f t f t
f f t t
f f f t

Construct a truth table for the statement.
~s^ ~q

s q ~s^ ~q

t t t
t f f
f t f
f f t

Construct a truth table for the statement.
c v ~(r ^ p)

c r p c v ~(r ^ p)
t t t t
t t f t
t f t t
t f f t
f t t f
f t f t
f f t t
f f f t

#### tkhunny

##### Moderator
Staff member
Please do not ever struggle with anything containing (s ^ ~s).

^ and v take two arguments. Do two at a time and make your life easier.

(p ^ ~q) ^ s

Just do (p ^ ~q) first and ignore s.

#### Mrspi

##### Senior Member
darleneporter said:
Can someone please help me, i am a little off with this question.

Construct a truth table for the statement.
s v (s ^ ~s)
&
(s ^ w)^(~w v t)

now, i am lost. also, could you also check the ones i have done below to see if i am on the right track:

Construct a truth table for the statement.
(p ^ ~q)^ s

p q s (p ^ ~q)^ s
t t t f
t t f f
t f t f
t f f f
f t t f
f t f t
f f t t
f f f t

Construct a truth table for the statement.
~s^ ~q

s q ~s^ ~q

t t t
t f f
f t f
f f t

Construct a truth table for the statement.
c v ~(r ^ p)

c r p c v ~(r ^ p)
t t t t
t t f t
t f t t
t f f t
f t t f
f t f t
f f t t
f f f t
The way I learned to do truth tables (which has served me WELL over half a century) is to make sure that you have everything represented by its own column....

I'll pick one of your problems as an example.

(p ^ ~q)^ s

As I see it, you will need columns for p, q, s, ~q, and s...as well as for (p ^ ~q) and [(p ^ ~q) ^ s]

Code:
p      q        s       ~q       (p ^ ~q)      (p ^ ~q) ^ s

T      T        T       F             F              F
T      T        F       F             F              F
T      F        T       T             T             T
T      F        F       T             T             F
F      T        T       F             F             F
F      T        F       F             F             F
F      F        T       T             F             F
F      F        F       T             F             F
Ok...the right-most column tells you when that statement is true, and when it is false.

When you are creating a truth table, "more" is better than "less"....make sure you have a column for EVERY value in your final statement.