SOLUTION: 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

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.

RELATED QUESTIONS
Could someone please help me with this truth table? Iam really struggling with this in... (answered by jim_thompson5910)

Construct a truth table for p ↔ (q ~p) and submit it to the Dropbox. Be sure to... (answered by Big Poop)

Construct a truth table for (p V q)right arrow ~p. Be sure to include all intermediate... (answered by MathLover1)

construct a truth table q--->(p v~q). and be sure to includ all intermediate steps in... (answered by Edwin McCravy)

construct a truth table for ~p->(p^~q). be sure to include all intermediate steps.... (answered by KIlges)

Construct a truth table for (~p ᴧ q) → p, be sure to include all your... (answered by solver91311)

construct a truth table for (~pVq)->p be sure to include all intermediate steps. thank (answered by jim_thompson5910)

Construct a truth table for (p q) ~p and it says to show all intermediate steps in your (answered by jim_thompson5910)

Hello, Can someone please help me with this truth statement, I am confused and I have... (answered by Fombitz,jerryguo41)