The truth table for the statement is:
s u t ~t (su) u→~t (su)(u→~t)
T T T F T T T
T T F T T F F
T F T F F T F
T F F T F F F
F T T F F T F
F T F T F F F
F F T F F T F
F F F T F F F .
To construct a truth table, we need to list all possible combinations of truth values for the individual propositions in the statement, and then evaluate the statement for each combination.
The statement in the image is:
(su)(u→~t)
This statement has three propositions: s, u, and t. So, our truth table will have four columns, one for each proposition and one for the overall statement.
Column 1 (s): This column lists all possible truth values for the proposition s.
Column 2 (u): This column lists all possible truth values for the proposition u.
Column 3 (t): This column lists all possible truth values for the proposition t.
Column 4 (~t): This column lists the negation of the proposition t.
Column 5 (su): This column lists the conjunction of the propositions s and u.
Column 6 (u→~t): This column lists the implication from u to ~t.
Column 7 ((su)(u→~t)): This column lists the conjunction of the propositions (su) and (u→~t).
To evaluate the implication u→~t, we use the following rule:
u→~t is true if and only if either u is false or ~t is true.
So, the implication u→~t is true in all cases except for when u is true and ~t is false.
To evaluate the conjunction (su)(u→~t), we use the following rule:
(su)(u→~t) is true if and only if both (su) and (u→~t) are true.
So, the conjunction (su)(u→~t) is only true in the case when s is true, u is true, and t is false.