Fill in the blanks for the missing values in the table.

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## Constructing a Truth Table

This section explores how to construct a truth table for the logical statement \(\sim t \rightarrow (u \land s)\).

### Truth Table

Below is the partially completed truth table for the expression. Your task is to fill in the blanks with the missing values.

| s   | t   | u   | \(\sim t\) | \(u \land s\) | \(\sim t \rightarrow (u \land s)\) |
|-----|-----|-----|-------------|---------------|-----------------------------------|
| T   | T   | T   | F           | T             | T                                 |
| T   | T   | F   | F           | F             | T                                 |
| T   | F   | T   | T           | T             |                                   |
| T   | F   | F   | T           | F             |                                   |
| F   | T   | T   | F           | F             | T                                 |
| F   | T   | F   | F           | F             | T                                 |
| F   | F   | T   | T           | F             |                                   |
| F   | F   | F   | T           | F             |                                   |

- \(s\), \(t\), and \(u\) are variables representing truth values. \(T\) stands for True, and \(F\) stands for False.
- \(\sim t\) represents the negation of \(t\).
- \(u \land s\) denotes the logical AND operation between \(u\) and \(s\).
- \(\sim t \rightarrow (u \land s)\) is a logical implication.
  
Your challenge is to determine the truth values for the missing entries in the table.
Transcribed Image Text:## Constructing a Truth Table This section explores how to construct a truth table for the logical statement \(\sim t \rightarrow (u \land s)\). ### Truth Table Below is the partially completed truth table for the expression. Your task is to fill in the blanks with the missing values. | s | t | u | \(\sim t\) | \(u \land s\) | \(\sim t \rightarrow (u \land s)\) | |-----|-----|-----|-------------|---------------|-----------------------------------| | T | T | T | F | T | T | | T | T | F | F | F | T | | T | F | T | T | T | | | T | F | F | T | F | | | F | T | T | F | F | T | | F | T | F | F | F | T | | F | F | T | T | F | | | F | F | F | T | F | | - \(s\), \(t\), and \(u\) are variables representing truth values. \(T\) stands for True, and \(F\) stands for False. - \(\sim t\) represents the negation of \(t\). - \(u \land s\) denotes the logical AND operation between \(u\) and \(s\). - \(\sim t \rightarrow (u \land s)\) is a logical implication. Your challenge is to determine the truth values for the missing entries in the table.
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