All, Some, and No — Syllogism Basics

• Meaning of All, Some, and No in logical statements about groups.
• Which conclusions validly follow and which are invalid reversals.
• To translate words into simple set pictures before answering.
• Intro syllogism skills for Class 5 reasoning and future competitive exams.

NCERT / CBSE link

CBSE Class 5 logical reasoning and Math-Magic 5, Chapter 6 (Be My Multiple, I'll Be Your Factor) both use set language (all/some/none of a group). Indian olympiad foundations start syllogisms at this level.

Level 1 — Quantifiers

Verbal: All = every member; Some = at least one (maybe all); No = zero overlap.

Symbolic: All A are B → every A is inside B circle.

Valid vs invalid (critical):

Level 2 — Reading carefully

Verbal: "Some students like cricket" does not mean some don't — "some" is at least one.

Real-life: All Class 5 students in school → some school students are Class 5 ✓.

Statement: All roses are flowers. Conclusion: All flowers are roses. Valid?

Step 1 — Roses inside flowers — many other flowers possible.
Step 2 — Cannot say all flowers are roses.
Answer: Invalid — reversal error.

Statement: Some books are stories. Conclusion: Some stories are books. Valid?

Step 1 — Overlap exists.
Step 2 — Overlap symmetric for "some."
Answer: Valid.

• All squares are rectangles. All rectangles squares? Yes/No?
• Some birds fly. Some flying things are birds? Yes/No?
• No reptiles are mammals. No mammals reptiles?
• Stretch: All A are B. All B are C. What follows about A and C?

Revision tip: Three-circle Venn on paper — shade "All A are B" then ask what you cannot conclude.

Open the Practice tab for graded questions on All, Some, and No.