Fill in the heading of the following truth table using any of p, q, ->, ?, V, and ^.
P q _____
T T T
T F F
F T T
F F T
p --> q
T, T......If I am in Paris, then I am in France. True.
T, F......If I am in Paris, then I am not in France. False.
F, T......If I am not in Paris, then I am in France. Possible (so it's "true")
F, F......If I am not in Paris, then I am not in France. Also possible, so it's true.
So it would be p q V ?? Because I have to fill in the heading (line) with any of those choices....
The proposition is
p --> q
The operator indicated in the third column is "->" (conditional)
ooooooh okay i get it now lol thank you :)
You're welcome!
To fill in the heading of the truth table, we need to identify the logical operator that represents the given conditions. Looking at the truth table, we can see that the result depends on the values of p and q.
In the first row, p and q are both true, and the result is also true. This suggests that the logical operator being used is the "AND" operator, represented by the symbol ^.
In the second row, p is true and q is false, resulting in a false value. This corresponds to the logical operator "AND" as well.
In the third row, p is false and q is true, yet the result is still true. This indicates that the logical operator is not simply "AND."
Finally, in the fourth row, both p and q are false, resulting in a true value.
Based on this information, we can conclude that the logical operator being used in this truth table is the "OR" operator, represented by the symbol V.
Hence, the heading of the truth table can be filled in as follows:
P q P V q
T T T
T F F
F T T
F F T