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End of Lesson
End of Lesson
In this lesson, we combine negation with implication (→) and biconditional (↔). These tables will show you how flipping inputs affects the results of these operators.
The first table explores every possible way of negating p or q in an implication. Pay attention to p → q versus q → p, and how their negations behave.
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) | q → p | ¬(q → p) | p → ¬q | ¬p → q | ¬p → ¬q |
|---|---|---|---|---|---|---|---|---|---|---|
| F | F | |||||||||
| F | T | |||||||||
| T | F | |||||||||
| T | T |
The second table focuses on p ↔ q and its variations under negation. Biconditional is true only when both statements agree (both true or both false).
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 |
Working through these tables helps you see the symmetry of implication and biconditional under negation. This is essential for understanding logical equivalence and contrapositive reasoning later.