Complete the following truth table. Use T for true and F for false. You may add more columns, but those added columns will not be graded. P 9 ~(p-q) Р q T T 0 OAD OVO T 0 0-0 0-0 T 0 X 5 ? F 0 F LL LL F FL

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### Introduction to Truth Tables with Conditional Statements

In this section, we will explore how to complete a truth table. A truth table helps us understand the logical relationships between different statements, represented by propositions.

#### Truth Table Instructions
Complete the following truth table. Use **T** for true and **F** for false. You may add more columns for your own analysis, but those added columns will not be graded.

Below is the template you need to complete:

| p   | q   | ∼(p → q) |
|-----|-----|----------|
| T   | T   |          |
| T   | F   |          |
| F   | T   |          |
| F   | F   |          |

Here’s what each notation means in the context of logic:
- **p**: Proposition 1
- **q**: Proposition 2
- **∼**: Logical NOT (negation)
- **→**: Logical implication or conditional ("if...then" statement)

In this exercise, you are asked to fill in the column for ∼(p → q).

#### Diagram Explanation
To the right of the truth table, there are checkboxes for filling in the truth values:
- **p** and **q** columns represent the truth values for each proposition.
- **∼**: Denotes negation.
- **→**: Denotes implication.
- The symbols represent the logical operations you are working with.

The three buttons below provide options to interact with the table:
- **X**: Likely used to indicate a final check or submission.
- **↺**: Indicates a refresh or reset option.
- **?**: Provides help or explanation.

#### Example Calculation:
For instance, in the first row where both p and q are true (T), you need to evaluate p → q and then negate it:
- p → q (T → T): This is true according to the implication rule.
- ∼(p → q): Negate the result above, so the result is false (F).

Buttons below the truth table provide further actions:
- **Explanation**: Offers detailed explanations.
- **Check**: Submit your current answers for evaluation.

Feel free to use these tools to ensure your answers are correct.
Transcribed Image Text:### Introduction to Truth Tables with Conditional Statements In this section, we will explore how to complete a truth table. A truth table helps us understand the logical relationships between different statements, represented by propositions. #### Truth Table Instructions Complete the following truth table. Use **T** for true and **F** for false. You may add more columns for your own analysis, but those added columns will not be graded. Below is the template you need to complete: | p | q | ∼(p → q) | |-----|-----|----------| | T | T | | | T | F | | | F | T | | | F | F | | Here’s what each notation means in the context of logic: - **p**: Proposition 1 - **q**: Proposition 2 - **∼**: Logical NOT (negation) - **→**: Logical implication or conditional ("if...then" statement) In this exercise, you are asked to fill in the column for ∼(p → q). #### Diagram Explanation To the right of the truth table, there are checkboxes for filling in the truth values: - **p** and **q** columns represent the truth values for each proposition. - **∼**: Denotes negation. - **→**: Denotes implication. - The symbols represent the logical operations you are working with. The three buttons below provide options to interact with the table: - **X**: Likely used to indicate a final check or submission. - **↺**: Indicates a refresh or reset option. - **?**: Provides help or explanation. #### Example Calculation: For instance, in the first row where both p and q are true (T), you need to evaluate p → q and then negate it: - p → q (T → T): This is true according to the implication rule. - ∼(p → q): Negate the result above, so the result is false (F). Buttons below the truth table provide further actions: - **Explanation**: Offers detailed explanations. - **Check**: Submit your current answers for evaluation. Feel free to use these tools to ensure your answers are correct.
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