Logic · Grades 8–10 · Unit 10
Truth Tree Builder
Enter the statements, break each connective yourself, and close a branch when it holds a statement and its negation. Check waits until you ask.
Decomposition rules
- ~~p stacks p on the same branch.
- p • q stacks p and q. ~(p ∨ q) stacks ~p and ~q. ~(p ⊃ q) stacks p and ~q.
- p ∨ q splits into p and q. ~(p • q) splits into ~p and ~q. p ⊃ q splits into ~p and q.
- p ≡ q splits into the pair p, q and the pair ~p, ~q. ~(p ≡ q) splits into p, ~q and ~p, q.
- Close a branch that contains any statement and its negation. A finished open branch is a way the statements can be true.