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End of Lesson
End of Lesson
In this lesson, we explore how negation interacts with conjunction (AND) and disjunction (OR). These are the building blocks of most compound statements.
The first table shows every possible combination of p and q when using negation and AND. Notice how each column flips when we negate p, q, or the entire statement. This will help you understand De Morgan’s laws.
Click on a cell to change its value to true or false. Press the submit button when you think you have gotten it right.
| p | q | ~p | ~q | p ∧ q | ~(p ∧ q) | p ∧ ~q | ~p ∧ q | ~p ∧ ~q |
|---|---|---|---|---|---|---|---|---|
| F | F | |||||||
| F | T | |||||||
| T | F | |||||||
| T | T |
This second table repeats the same process but with OR instead of AND. Compare the last column with the one above and observe how ~(p ∨ q) behaves differently from ~(p ∧ q).
Click on a cell to change its value to true or false. Press the submit button when you think you have gotten it right.
| p | q | ~p | ~q | p ∨ q | ~(p ∨ q) | p ∨ ~q | ~p ∨ q | ~p ∨ ~q |
|---|---|---|---|---|---|---|---|---|
| F | F | |||||||
| F | T | |||||||
| T | F | |||||||
| T | T |
By filling these tables, you will see exactly how negation interacts with conjunction and disjunction. This is the foundation for simplifying and transforming logical statements later.