Syllogisms
0/10 problems solved
Formulas & 30-Second Shortcut Tricks
Formulas
- All + All = All (All A are B, All B are C ⇒ All A are C)
- All + No = No; Some + All = Some; Some + No = Some-Not
- No definite conclusion from: Some + Some, Some + Some-Not, No + No
- Either-or case: two complementary possibilities (Some/No) on the same pair
Shortcuts
- Draw Venn circles minimally — only overlap where a statement forces it.
- 'Some A are B' ⇒ 'Some B are A' always (conversion).
- 'All A are B' ⇒ 'Some B are A', but NOT 'All B are A'.
Practice problems
Statements: All cats are dogs. All dogs are birds. Conclusions: I. All cats are birds. II. Some birds are cats.
Statements: Some pens are books. No book is a bag. Conclusions: I. Some pens are not bags. II. No pen is a bag.
Statements: All roses are flowers. Some flowers are red. Conclusions: I. Some roses are red. II. All red things are flowers.
Statements: No apple is a mango. All mangoes are fruits. Conclusions: I. Some fruits are not apples. II. No apple is a fruit.
Statements: Some teachers are singers. Some singers are dancers. Conclusions: I. Some teachers are dancers. II. Some dancers are singers.
Statements: All chairs are tables. No table is a desk. Conclusions: I. No chair is a desk. II. Some desks are chairs.
Statements: Some boys are tall. Some tall people are smart. Conclusions: I. Some boys are smart. II. All smart people are boys.
Statements: All engineers are graduates. All graduates are literate. Conclusions: I. All engineers are literate. II. All literate people are engineers.
Statements: No car is a bus. No bus is a train. Conclusions: I. No car is a train. II. Some trains are cars.
Statements: Some phones are laptops. All laptops are gadgets. Conclusions: I. Some phones are gadgets. II. Some gadgets are laptops.
Syllogisms Speed Test
1 minute per question. Use the palette to jump around; you'll see time spent on every question at the end.