Practise eight fixed challenges, from negation to expressions with three propositions. Fill in operation cells and check your table, with no random selection.
Complete ¬p by reversing the value of p.
Propositions: p. Inputs are already filled in. Choose T (true) or F (false) for each operation cell; — means unanswered.
| Row | p | ¬p |
|---|---|---|
| 1 | F | |
| 2 | T |
Read the input propositions in each row and evaluate the operations, starting with parentheses and intermediate columns. T means true; F means false. An unanswered cell is different from an F answer.
The order matches the generator: all inputs start false and the rightmost variable alternates fastest. Two propositions need 2² = 4 rows; three need 2³ = 8. One proposition has two rows.
¬ means not; ∧ means and; ∨ means inclusive or; → means if… then; ↔ means if and only if. Negation reverses the value, conjunction requires both to be true, and disjunction requires at least one to be true.
A conditional is false only for T → F. A biconditional is true when the values match. The catalogue displays p, q and r; internally it reuses the generator's evaluator with P, Q and R.
For inputs (p,q) = (F,F), (F,T), (T,F), (T,T), conjunction p ∧ q gives F, F, F, T. Negating that column, ¬(p ∧ q) gives T, T, T, F. This example is separate from the challenges in the practice board.
Check table preserves all answers and identifies correct, incorrect and unanswered cells with text, not just colour. Correct any mistakes before moving on. Each incorrectly answered cell adds one error per attempt; identical checks do not count it again.
Revealing the solution counts as help, not as an unaided correct answer. Retry clears the current attempt while keeping the exercise. Next exercise follows the fixed catalogue order. Counters apply to this session, with no account or permanent storage.