Syllogism

Reasoning Ability · Core Logical Tools

Useful for: SSC CGL, Railway RRB, IBPS Banking, KVS, NVS, OTET, BPSC TRE, UGC NET

and 21 more exams

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Overview

Syllogism tests which conclusions must follow from given statements, assuming the statements are true even if unrealistic.

Key points

All A are B + All B are C → All A are C.
All A are B + No B is C → No A is C.
Some A are B + All B are C → Some A are C.
Some A are B + No B is C → Some A are not C.
Two "Some" statements give no definite conclusion between the end terms.

Explanation

"Some A are B" implies "Some B are A" (conversion).
"All A are B" implies "Some A are B" and "Some B are A", but not "All B are A".
A conclusion follows only if it is true in every possible diagram.
Complementary pair: if neither "Some A are C" nor "No A is C" follows definitely, then "either–or" follows.

Step by step

Draw a Venn diagram for each statement.
Find what is always true.
Accept only certain conclusions.

Examples

All pens are books; some books are bags. "Some pens are bags" does not follow (the overlap may not include pens).
All A are B; no B is C → "No A is C" follows.
Some A are B; no B is C → "Some A are not C" follows.

Traps and advanced points

Trap: Using real-world knowledge instead of the statements.
Trap: Assuming "All A are B" means "All B are A".
Trap: Accepting a conclusion that is only possible, not certain.

Quick revision

All + All = All; All + No = No.
Some + All = Some; Some + No = Some not.
Some + Some = no conclusion.

Practice MCQs

If the sets “Pilots” and “Volunteers” overlap partly, which statement best describes the Venn diagram?
1. No pilots can be volunteers
2. All volunteers are pilots
3. All pilots are volunteers
4. Some pilots may be volunteers
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Answer: (d) Some pilots may be volunteers. Partial overlap means intersection exists but neither set fully contains the other.
If the sets “Teachers” and “Voters” overlap partly, which statement best describes the Venn diagram?
1. Some teachers may be voters
2. All teachers are voters
3. No teachers can be voters
4. All voters are teachers
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Show answer
Answer: (a) Some teachers may be voters. Partial overlap means intersection exists but neither set fully contains the other.
All analysts are learners. Some analysts are award-winning. Which conclusion definitely follows?
1. All award-winning people are analysts
2. Some award-winning people are learners
3. No analysts is award-winning
4. All learners are analysts
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Answer: (b) Some award-winning people are learners. If some A are award-winning and all A are B, then some award-winning are B.
All artists are professionals. Some artists are experienced. Which conclusion definitely follows?
1. All professionals are artists
2. Some experienced people are professionals
3. No artists are experienced
4. All experienced people are artists
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Show answer
Answer: (b) Some experienced people are professionals. If some A are experienced and all A are B, then some experienced are B.
All bankers are graduates. Some bankers are trained. Which conclusion definitely follows?
1. All graduates are bankers
2. No bankers are trained
3. All trained people are bankers
4. Some trained people are graduates
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Answer: (d) Some trained people are graduates. If some A are trained and all A are B, then some trained are B.
All architects are workers. Some architects are award-winning. Which conclusion definitely follows?
1. No architects is award-winning
2. All workers are architects
3. Some award-winning people are workers
4. All award-winning people are architects
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Show answer
Answer: (c) Some award-winning people are workers. If some A are award-winning and all A are B, then some award-winning are B.
All drivers are team members. Some drivers are trained. Which conclusion definitely follows?
1. Some trained people are team members
2. All trained people are drivers
3. All team members are drivers
4. No drivers are trained
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Show answer
Answer: (a) Some trained people are team members. If some A are trained and all A are B, then some trained are B.
All doctors are creative people. Some doctors are young. Which conclusion definitely follows?
1. No doctors are young
2. All young people are doctors
3. Some young people are creative people
4. All creative people are doctors
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Answer: (c) Some young people are creative people. If some A are young and all A are B, then some young are B.
All architects are workers. Some architects are urban. Which conclusion definitely follows?
1. All workers are architects
2. All urban people are architects
3. No architects are urban
4. Some urban people are workers
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Answer: (d) Some urban people are workers. If some A are urban and all A are B, then some urban are B.
All writers are workers. Some writers are urban. Which conclusion definitely follows?
1. All urban people are writers
2. All workers are writers
3. Some urban people are workers
4. No writers are urban
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Answer: (c) Some urban people are workers. If some A are urban and all A are B, then some urban are B.
All lawyers are trained people. Some lawyers are urban. Which conclusion definitely follows?
1. All trained people are lawyers
2. All urban people are lawyers
3. Some urban people are trained people
4. No lawyers are urban
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Answer: (c) Some urban people are trained people. If some A are urban and all A are B, then some urban are B.
All athletes are volunteers. Some athletes are experienced. Which conclusion definitely follows?
1. All volunteers are athletes
2. No athletes are experienced
3. Some experienced people are volunteers
4. All experienced people are athletes
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Show answer
Answer: (c) Some experienced people are volunteers. If some A are experienced and all A are B, then some experienced are B.
All students are readers. Some students are young. Which conclusion definitely follows?
1. No students are young
2. Some young people are readers
3. All readers are students
4. All young people are students
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Answer: (b) Some young people are readers. If some A are young and all A are B, then some young are B.
All engineers are learners. Some engineers are young. Which conclusion definitely follows?
1. No engineers are young
2. All learners are engineers
3. All young people are engineers
4. Some young people are learners
Read chapter notes · Similar questions
Show answer
Answer: (d) Some young people are learners. If some A are young and all A are B, then some young are B.
All drivers are team members. Some drivers are urban. Which conclusion definitely follows?
1. No drivers are urban
2. Some urban people are team members
3. All team members are drivers
4. All urban people are drivers
Read chapter notes · Similar questions
Show answer
Answer: (b) Some urban people are team members. If some A are urban and all A are B, then some urban are B.

Syllogism

Overview

Key points

Explanation

Step by step

Examples

Traps and advanced points

Quick revision

Practice MCQs

More topics in this chapter