- Asked 5/9
- 2071 Bhadra · 3 marks
Tableau for (p∧¬q)→s
Draw the tableau for the formula Φ = (p∧¬q)→s, where ¬ denotes the negation of a variable, ∧ denotes the conjunction of variables and → denotes the implication.
Formula Φ = (p ∧ ¬q) → s.
Rules. A → B is a β-formula and splits into ¬A | B. Then ¬(p ∧ ¬q) is a β-formula and splits into ¬p | ¬¬q, and ¬¬q is replaced by q.
Tableau
(p ∧ ¬q) → s
/ \
¬(p ∧ ¬q) s
/ \ o
¬p ¬¬q
o |
q
o
| Branch | Literals | Status |
|---|---|---|
| 1 | ¬p | open |
| 2 | q | open |
| 3 | s | open |
All three branches are open (no complementary pair), so Φ is satisfiable. The models are: p = F; or q = T; or s = T.
✓ Answer checked by Claude Opus 5.5 (high effort)
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