Syllogisms
Syllogisms represent groups as sets and ask whether a conclusion must follow from statements such as “All A are B”, “No B are C”, or “Some A are B”. ReasonUp uses modern set logic: an “All” statement alone does not assume that members of that group exist.
Common patterns
- Universal inclusion chains such as All A are B and All B are C
- Exclusion combined with inclusion
- Existential statements beginning with Some
- Shared-superclass traps where two groups need not overlap
- Non-transitive existential overlaps
Worked example
Question: All roses are flowers. All flowers are plants. Must all roses be plants?
Answer: Yes
Roses are a subset of flowers, and flowers are a subset of plants, so roses must also be a subset of plants.
How to approach Syllogisms
- Translate statements into sets — Treat “All”, “No” and “Some” as precise set relationships instead of relying on everyday associations between the words.
- Follow only guaranteed links — Chain universal relationships carefully and do not create an overlap or existence claim that the premises never state.
- Test the conclusion for necessity — Ask whether every arrangement satisfying the premises must also satisfy the conclusion; if one valid counterexample exists, it does not necessarily follow.