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Propositional Logic Calculator

Online sufficient/necessary checker: use set inclusion to decide the relation between p and q.

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p⇒q sufficient; p⇔q iff
Commas
Commas

📖 Tutorial | Conditions

1. Definition
p⇒q: p is sufficient for q, q is necessary for p; p⇔q is iff.
2. Formula & Notation
⇒, ⇔Implies, equivalent
3. Properties & Laws
  • A⊆B means p sufficient;
  • B⊆A means p necessary;
  • Both ways is iff;
  • Contrapositive has equal truth.
4. Steps
  1. Enter sets for p and q;
  2. Click "Check";
  3. Or click "Load Example".
5. Worked Examples
Example: A{1,2}⊆B{1,2,3,4}: sufficient not necessary.
6. Common Pitfalls
Watch the direction;
Set inclusion maps to conditions;
Need both ways for iff.

❓ FAQ | Conditions

Sufficient?
p⇒q.
Necessary?
q⇒p.
Iff?
Equivalent.
Contrapositive?
Same truth.
Example?
Sufficient.
A⊆B?
Sufficient.