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  1. LPU MCA Semester 1
  2. PEA515
  3. Unit 3

PEA515 · Unit 3: Logical reasoning

Syllogism using logical Venn diagrams

30 practice questions · in the MTE and ETE syllabus

Practise this topicPractise this topic

Key points

  • A conclusion must hold in every valid diagram
  • No A is B converts to No B is A
  • Some A are not B cannot be reversed
  • All A are B implies Some B are A

Four statement types appear: All A are B, No A is B, Some A are B, and Some A are not B. Each class named is taken to be non-empty.

Conversions that always hold: All A are B gives Some B are A (and Some A are B); Some A are B gives Some B are A; No A is B gives No B is A. Some A are not B has no converse.

Method: draw the most general Venn diagram for the statements, then check each conclusion against every diagram you can draw. A conclusion follows only if it is true in all of them. If a diagram exists in which it is false, it does not follow.

Standard answer patterns: "Only I follows", "Only II follows", "Both follow", "Neither follows".

Example: All flowers are roses and No roses are trees. "Some roses are flowers" follows, but "All roses are trees" is false in every diagram.

Exam trap: accepting a conclusion because one diagram supports it, instead of requiring all diagrams.

Try two questions

Question 1 · Tier 3, Apply

Statements: No trees are flowers. No trees are roses. Conclusions: I. No trees are flowers. II. Some flowers are trees. Which of the following is correct?

  1. Only conclusion II follows
  2. Both conclusions I and II follow
  3. Only conclusion I follows
  4. Neither conclusion I nor II follows
Show the answer

C. A conclusion follows only if it is true in every Venn diagram consistent with the statements (every class named is taken to be non-empty).

Why not A: Credits conclusion II but misses or wrongly accepts conclusion I.

Why not B: Accepts both without testing each against every possible Venn diagram.

Why not D: Rejects both, missing a conclusion that is supported.

Question 2 · Tier 4, Analyse

Statements: No trains are buses. All cars are buses. Conclusions: I. No trains are cars. II. Some trains are not buses. Which of the following is correct?

  1. Only conclusion I follows
  2. Both conclusions I and II follow
  3. Only conclusion II follows
  4. Neither conclusion I nor II follows
Show the answer

B. A conclusion follows only if it is true in every Venn diagram consistent with the statements (every class named is taken to be non-empty).

Why not A: Credits conclusion I but misses or wrongly accepts conclusion II.

Why not C: Credits conclusion II but misses or wrongly accepts conclusion I.

Why not D: Rejects both, missing a conclusion that is supported.