The truth table for the statement (~svt) u shows that the statement is T when either ~svt or u is T, and F otherwise. This means that the statement is T when either s and t are both F, or when u is T.
To construct a truth table for the statement, we first need to identify the different propositions in the statement. The propositions in the statement are:
- s
- t
- ~t (the negation of t)
- ~s (the negation of s)
- ~svt (the negation of s or t)
- u
We then need to determine the truth value of each proposition for each possible combination of truth values for the other propositions.
This is shown in the following truth table:
s t ~t ~s ~svt ~svt u
T T F F F T
T F T F F T
F T F T T F
F F T T T F
The last column of the truth table shows the truth value of the statement (~svt) u.
The statement is T when either ~svt or u is T, and F otherwise.
Here is a more detailed explanation of each row of the truth table:
Row 1: s and t are both T, so ~t and ~s are both F. ~svt is F because s is T, and u is irrelevant.
Therefore, the statement (~svt) u is T.
Row 2: s is T and t is F, so ~t is T and ~s is F.
~svt is F because s is T.
However, u is also T, so the statement (~svt) u is T.
Row 3: s is F and t is T, so ~t is F and ~s is T.
~svt is T because s is F.
However, u is F, so the statement (~svt) u is F.
Row 4: s and t are both F, so ~t and ~s are both T.
~svt is T because both s and t are F.
Therefore, the statement (~svt) u is T.
In conclusion, the truth table for the statement (~svt) u shows that the statement is T when either ~svt or u is T, and F otherwise.