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Construct a truth table for the statement.
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Fill in the missing values in the table. Fill in the blanks below.

Answer 1

In the truth table for
`\(\sim t \leftrightarrow(s \lor \sim u)\)` when
`\(s = T\)`,
`\(t = T\)`, and u = T, the values of
`\(\sim t\), \(\sim u\), \(s \lor \sim u\)`, and
`\(\sim t \leftrightarrow (s \lor \sim u)\)` are
`\(F\), \(F\), \(T\)`, and
`\(F\)`, respectively.

To construct the truth table for the statement
`\(\sim t \leftrightarrow (s \lor \sim u)\)`, we need to fill in the missing values.

1.
`\(\sim t\)` is the negation of t, so
`\(\sim t\)` is F.

2.
`\(\sim u\)` is the negation of u, so
`\(\sim u\)` is F.

3.
`\(s \lor \sim u\)` is the logical OR between s and
`\(\sim u\)`, so
`\(s \lor \sim u\)` is T.

4.
`\(\sim t \leftrightarrow (s \lor \sim u)\)` is the biconditional between
`\(\sim t\)` and
`\(s \lor \sim u\)`. Since
`\(\sim t\)` and
`\(s \lor \sim u\)` have different truth values, this evaluates to F.

The final table has been attached.

So, the filled-in values are
`\(\sim t = F\)`,
`\(\sim u = F\)`,
`\(s \lor \sim u = T\)`, and
`\(\sim t \leftrightarrow (s \lor \sim u) = F\)`.