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

PEA515 · Unit 3: Logical reasoning

Syllogism possibility questions

30 practice questions · in the MTE and ETE syllabus

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Key points

  • Possibility means true in at least one valid diagram
  • Anything that follows definitely is also possible
  • A contradiction of a premise is never possible
  • Test by trying to redraw the diagram

A possibility conclusion asks whether the statement is true in at least one valid diagram. This is the opposite test to ordinary syllogism: one supporting diagram is enough, and one is also all you need to refute "cannot be true".

Method:

  1. Draw the diagram forced by the statements.
  2. Try to adjust it (merge, overlap or separate classes) so that the conclusion becomes true without breaking any statement.
  3. If you can, the possibility holds; if every adjustment contradicts a statement, it does not.

A statement that is definitely true is also a possibility. A statement that contradicts a premise (for example, "Possibility that all A are B" when the premises say No A is B) is never a possibility.

Example: Some phones are laptops and All devices are laptops. "Possibility that no phones are devices" holds, but "Possibility that no laptops are devices" fails because devices are laptops.

Exam trap: treating "possibility" as "definitely follows".

Try two questions

Question 1 · Tier 3, Apply

Statements: All berries are bananas. No berries are grapes. Possibility conclusions: I. Possibility that all bananas are grapes. II. Possibility that all berries are grapes. Which of the following is correct?

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

B. A possibility conclusion is accepted if at least one Venn diagram consistent with the statements makes it true.

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: Accepts both without testing each against every possible Venn diagram.

Question 2 · Tier 4, Analyse

Statements: Some comets are planets. Some planets are stars. Possibility conclusions: I. Possibility that some stars are comets. II. Possibility that all stars are planets. 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 possibility conclusion is accepted if at least one Venn diagram consistent with the statements makes it true.

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.