Question 568976: Construct a truth table for (p ^ q) -> ~q Be sure to include all intermediate steps on your table.
Because this has no assigned statements to it, I am confused as to how I would solve this.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you create a truth table that includes columns for:
p
q
~q
(p ^ q)
(p ^ q) -> ~q
your table would look like this:
your table needs 2 rows per variable.
the number of rows in your table is equal to 2 raised to the power of the number of variables.
in this case the number of rows is 2^2 = 4
if 3 variables, the number of rows is 2^3 = 8
if 4 variables, the number of rows is 2^4 = 16
this is required to capture all of the possible combinations for all of the variables in combination.
your table only requires 2 rows because you only have 2 variables.
they are p and q.
the possible combinations for p and q are:
TT, TF, FT, FF
if you have 3 variables, then the total combinations would be 8 as shown here:
TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF
you only have 2 variables so we have 4 rows only as shown in the table.
~q is the revere of q.
when q is true, ~q is false.
when q is false, ~q is true.
this can be seen in the table.
(p ^ q) is true if both p and q are true, otherwise it is false.
this is also shown in the table.
the only time (p ^ q) is true is when p is true and q is true.
(p ^ q) -> ~q is only false if (p ^ q) is true and ~q is false.
otherwise it is true.
this can also be shown in the table.
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