how to construct a truth table for q w/upside down v~p, using the following:
P: this is an orange
q: the monkey is tall
To construct a truth table for the expression q w/upside down v~p, where P represents "this is an orange" and q represents "the monkey is tall," you need to consider all the possible combinations of truth values for P and q.
There are 2 variables in this expression, so there are 2^2 = 4 possible combinations of truth values.
Step 1: Create a table with columns for P, q, ~p, and q w/upside down v~p.
Step 2: Fill in the P and q columns with all possible combinations of truth values for P and q. In this case, you will have:
P | q
------------
T | T
T | F
F | T
F | F
Step 3: Fill in the ~p column. ~p represents the negation of P. Negate the truth values in the P column to obtain ~p:
P | q | ~p
-----------------------------
T | T | F
T | F | F
F | T | T
F | F | T
Step 4: Fill in the q w/upside down v~p column. The upside down v symbol represents logical disjunction (OR). Apply the OR operation to the q and ~p values:
P | q | ~p | q w/upside down v~p
---------------------------------------
T | T | F | T
T | F | F | F
F | T | T | T
F | F | T | F
This completes the truth table for the expression q w/upside down v~p using the given variables P and q.