Universal–universal with exclusion: From 'All flowers are trees' and 'No fruit is tree', assess whether the conclusions (I) 'No fruit is flower' and (II) 'Some trees are flowers' follow beyond doubt in standard syllogism.
Verbal Reasoning
Logical Deduction
Difficulty: Easy
Choose an option
Answer
Correct Answer: Both I and II follow
Explanation
Given data
- Premise 1: All Flowers ⊆ Trees.
- Premise 2: No Fruit is a Tree (Fruit ∩ Tree = ∅).
- Conclusions: (I) No Fruit is a Flower. (II) Some Trees are Flowers.
Concept/Approach
(I) is a standard syllogistic inference: if Flowers are among Trees and Fruits are excluded from Trees, then Fruits are excluded from Flowers. (II) is an existential import commonly assumed in aptitude syllogisms: if 'All Flowers are Trees' and Flowers exist, then at least some Trees are Flowers.
Step-by-step calculation/logic
1) From Premise 1, Flower ⊆ Tree.2) From Premise 2, Fruit ∩ Tree = ∅ ⇒ Fruit cannot overlap any subset of Tree, including Flowers.3) Hence (I) 'No Fruit is Flower' is compelled.4) If at least one Flower exists (typical test assumption), that Flower is a Tree ⇒ 'Some Trees are Flowers' (II) holds.Verification/Alternative
Venn diagram: put Flowers wholly inside Trees; draw Fruit disjoint from Trees. Then both conclusions are visually evident.
Common pitfalls
- Rejecting (II) due to confusion about existential import; aptitude syllogism sets usually accept it.
Final AnswerBoth I and II follow.