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ABHYAS PREP: REASONING CORE · SYLLOGISM

Syllogisms: which conclusions follow

A conclusion follows only if it is true in every Venn diagram the statements allow. Try to draw one diagram that breaks it; if you cannot, it follows.

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Worked examples

Example 1 · level 1

Statements: No writers are singers. No singers are dancers. Conclusions: I. Some singers are writers. II. Some writers are dancers.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either I or II follows
  4. Neither I nor II follows
  5. Both I and II follow
Show solution
  1. Statements as a diagram: No writers are singers; No singers are dancers.
  2. I (Some singers are writers) is false in at least one diagram the statements allow, so it is not definite.
  3. II (Some writers are dancers) is false in at least one diagram the statements allow, so it is not definite.
  4. So the answer is: Neither I nor II follows.

Answer: Neither I nor II follows

Example 2 · level 2

Statements: Some ponds are seas. Some seas are rivers. Conclusions: I. All seas are ponds. II. Some seas are ponds.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either I or II follows
  4. Neither I nor II follows
  5. Both I and II follow
Show solution
  1. Statements as a diagram: Some ponds are seas; Some seas are rivers.
  2. I (All seas are ponds) is false in at least one diagram the statements allow, so it is not definite.
  3. II (Some seas are ponds) is true in every diagram the statements allow.
  4. So the answer is: Only conclusion II follows.

Answer: Only conclusion II follows

Example 3 · level 3

Statements: All stools are beds. All beds are chairs. Conclusions: I. No beds being stools is a possibility. II. Some chairs are beds.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Either I or II follows
  4. Neither I nor II follows
  5. Both I and II follow
Show solution
  1. Statements as a diagram: All stools are beds; All beds are chairs.
  2. I: I (No beds being stools is a possibility) fails as a possibility here (either it is impossible, or it is already definite).
  3. II (Some chairs are beds) is true in every diagram the statements allow.
  4. So the answer is: Only conclusion II follows.

Answer: Only conclusion II follows

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