Syllogism for RRB NTPC: Venn diagrams, either–or and possibility

A syllogism gives two or three statements and two conclusions. You decide which conclusions definitely follow. The statements are often absurd on purpose ("All cups are birds"), because the question is testing logic, not general knowledge. Accept every statement as true, and forget what you know about the real world.

The good news is that syllogism has a small, closed set of rules. Once you can draw the diagrams quickly and know the either–or pairs, most questions take under a minute.

Where it fits in RRB NTPC

Syllogism is listed in the General Intelligence and Reasoning syllabus for both CBT stages. Questions usually follow the standard format: statements, two conclusions, and options such as "only I follows", "only II follows", "either I or II follows", "neither follows" and "both follow".

The four statement types

"Some" means "at least one, possibly all". That is the single most important word in the topic. "Some A are B" does not rule out "All A are B".

What each statement lets you conclude

Two reversals trap people. "All A are B" does not reverse to "All B are A" (all dogs are animals, but not all animals are dogs). "Some A are not B" does not reverse at all.

The method

1. Draw the simplest diagram that fits every statement.
2. For each conclusion, ask: "Is this true in every diagram I could draw?"
3. Try to break the conclusion: redraw the circles in a legal way that makes it false. If you can, it does not follow.
4. If neither conclusion follows, check the either–or test below.

The either–or test

Choose "either I or II follows" only when all three conditions hold:

• Both conclusions are about the same two groups.
• Neither follows on its own.
• They form a complementary pair, so exactly one of them must be true.

"Some A are B" and "All A are B" are not a pair. Both can be false together (when no A is B).

Worked examples

Example 1: All dogs are animals. All animals are living things.

• I. All dogs are living things. Follows (dog inside animal inside living thing).
• II. Some living things are dogs. Follows (the reverse of "All dogs are living things").
• Answer: both follow.

Example 2: Some pens are books. All books are papers.

• I. Some pens are papers. Follows. The pens that are books sit inside papers.
• II. All papers are pens. Does not follow. Papers can extend far beyond pens.
• Answer: only I.

Example 3: No cat is a dog. All dogs are pets.

• I. No cat is a pet. Does not follow. Cats can overlap the pet circle outside the dog part.
• II. Some pets are not cats. Follows. The pets that are dogs are not cats.
• Answer: only II.

Example 4: All chairs are tables. Some tables are desks.

• I. Some chairs are desks. II. No chair is a desk.
• Neither is certain: the desk circle may or may not reach inside the chair circle. But the two form a some / no pair about chairs and desks, so one must be true.
• Answer: either I or II follows.

Example 5: Some roads are rails. No rail is a bridge.

• I. Some roads are not bridges. Follows. The roads that are rails cannot be bridges.
• II. Some bridges are not roads. Does not follow. Every bridge could sit inside the road circle, away from the rails.
• Answer: only I.

Possibility questions

Some papers phrase a conclusion as "X is a possibility". Here the test flips: the conclusion is valid if you can draw at least one legal diagram where it is true.

Example 6: No A is B. All B are C.

• I. All C being A is a possibility. Not possible. If every C were A, the B circle (inside C) would also be inside A, but no A is B.
• II. Some C being A is a possibility. Possible. A can overlap the part of C outside B.
• Answer: only II.

Common mistakes

• Using real-world knowledge instead of the given statements.
• Reversing "All A are B" into "All B are A".
• Reading "some" as "only some", which wrongly rules out "all".
• Choosing either–or for two conclusions about different groups, or for a some / all pair.
• Stopping at one diagram. A conclusion true in your first drawing may fail in another.

Practice set

1. All roses are flowers. Some flowers are red. I. Some roses are red. II. All roses are red.
2. All students are readers. All readers are learners. I. All students are learners. II. Some learners are students.
3. No bird is a fish. Some fish are pets. I. Some pets are not birds. II. No pet is a bird.
4. Some cups are plates. Some plates are bowls. I. Some cups are bowls. II. No cup is a bowl.
5. All keys are locks. No lock is a door. I. No key is a door. II. Some doors are not keys.
6. Some trains are buses. All buses are cars. I. Some cars are trains. II. All trains are cars.
7. All coins are notes. All notes are bags. I. All bags are coins. II. Some bags are not coins.
8. All mangoes are fruits. No fruit is a stone. I. Some stones being mangoes is a possibility. II. Some fruits not being mangoes is a possibility.

Answers:

1. Neither follows. The red part of flowers may miss roses entirely. "Some" and "all" are not a complementary pair, so it is not either–or.
2. Both follow. Students sit inside readers, inside learners.
3. Only I. Pets that are fish cannot be birds. Other pets could still be birds, so II fails.
4. Either I or II. Cups and bowls may or may not meet; I and II are a some / no pair.
5. Both follow. Keys sit inside locks, and locks never touch doors, so no key is a door. Every door lies outside keys.
6. Only I. The trains that are buses are cars. Other trains may lie outside cars.
7. Either I or II. Bags may equal coins or be larger; I and II are an all / some-not pair.
8. Only II. A mango is a fruit and no fruit is a stone, so no stone can be a mango. Fruits beyond mangoes are allowed.

What to do next

• Memorise the two complementary pairs: some / no and all / some-not.
• For your next 20 questions, try to break every conclusion before accepting it.
• Revise Venn diagrams, which use the same circles with numbers.
• Then move to statements and conclusions, where the logic is looser and the reading matters more.