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Logical Possibility / Implied Relation

Introduction

The Logical Possibility / Implied Relation pattern tests your ability to determine whether a relationship between two elements can be logically possible - even if it is not directly stated. In this type of question, you must evaluate whether a conclusion may be true based on the given statements, without directly contradicting them.

This is different from typical syllogism questions where conclusions must necessarily follow. Here, we focus on what is possible - what the data allows - rather than what must be true.

Pattern: Logical Possibility / Implied Relation

Pattern

These questions involve reasoning from given premises to find relationships that are possible but not explicitly stated. You will often encounter terms like “can be true”, “may be possible”, or “can be implied”.

  • If a conclusion does not contradict any premise, it is possible.
  • If a conclusion directly opposes a given premise, it is impossible.
  • If a conclusion logically fits with the premises but is not guaranteed, it is logically possible.
  • Some questions may involve implied links across multiple statements - e.g., A → B and B → C implies that A → C is possible.

Step-by-Step Example

Question

Statements:
1️⃣ All actors are humans.
2️⃣ Some humans are artists.

Which of the following is logically possible?

A. All actors are artists.
B. Some actors are artists.
C. No actor is an artist.
D. Both A and B are impossible.

Solution

  1. Step 1: Interpret the statements

    All actors ⊂ humans; Some humans ↔ artists. This means there is a partial overlap between humans and artists.

  2. Step 2: Evaluate possibilities

    Since all actors are within humans, and some humans are artists, it’s possible that some actors are also artists (Option B). However, we cannot say “All actors are artists” because the premises don’t confirm that.

  3. Step 3: Check contradictions

    Nothing in the statements forbids actors from being artists, so “Some actors are artists” is logically possible.

  4. Final Answer:

    Some actors are artists. → Option B

  5. Quick Check:

    If the conclusion doesn’t violate any given premise, it is logically possible. ✅

Quick Variations

  • 1. Implied Relation Type: A link may not be direct but inferred through a chain (A → B → C ⇒ A → C possible).
  • 2. Possibility vs Certainty: If data allows multiple interpretations, the conclusion is only possible, not definite.
  • 3. Contradictory Premises: If a conclusion contradicts any universal negative or positive, it becomes impossible.
  • 4. Reversal Test: Always check if the reverse relation would still hold logically - this helps detect impossibilities.

Trick to Always Use

  • Look for what is not ruled out by the statements - that’s the “possible” zone.
  • When in doubt, draw quick Venn circles to test overlap and separation.
  • Remember: “Possible” means not contradicting, not necessarily “true.”
  • Chain reasoning helps: if A → B and B → C, then A → C is possible.

Summary

Summary

  • Identify all direct and indirect relations among terms.
  • A conclusion is possible if it fits logically without breaking any rule.
  • Universal negatives (“No”) block possibilities completely.
  • Use chaining logic (A → B → C) to find implied possibilities.

Example to remember:
All A are B; Some B are C ⇒ It is possible that Some A are C. ✅

Practice

(1/5)
1. Statements: 1️⃣ All poets are thinkers. 2️⃣ Some thinkers are dreamers.<br>Which of the following is logically possible?
easy
A. All poets are dreamers
B. Some poets are dreamers
C. No poet is a dreamer
D. All dreamers are poets

Solution

  1. Step 1: Analyze

    All Poets ⊂ Thinkers; Some Thinkers ↔ Dreamers ⇒ There is an overlap between Thinkers and Dreamers.

  2. Step 2: Check possibilities

    Since all Poets are Thinkers, and Thinkers overlap with Dreamers, it is possible that some Poets belong to the Dreamer group.

  3. Final Answer:

    Some poets are dreamers. → Option B

  4. Quick Check:

    No contradiction exists; ‘Some’ always remains a logical possibility. ✅
Hint: ‘All + Some’ ⇒ ‘Some’ is always possible unless explicitly denied.
Common Mistakes: Assuming overlap is definite rather than possible.
2. Statements: 1️⃣ Some engineers are artists. 2️⃣ No artist is a lawyer.<br>Which of the following is logically possible?
easy
A. Some engineers are lawyers
B. All engineers are lawyers
C. Some engineers are not lawyers
D. No engineer is a lawyer

Solution

  1. Step 1: Decode

    Some Engineers ↔ Artists; No Artist ↔ Lawyer ⇒ Artists and Lawyers are disjoint.

  2. Step 2: Test each option

    Engineers who are Artists cannot be Lawyers, so it’s certain that some Engineers (those Artists) are not Lawyers - hence it’s logically possible.

  3. Final Answer:

    Some engineers are not lawyers. → Option C

  4. Quick Check:

    ‘Some overlap + No relation’ ⇒ Some outside relation possible. ✅
Hint: If one part of a group is blocked from another, ‘Some not’ becomes possible.
Common Mistakes: Treating possibility as impossibility when partial exclusion is implied.
3. Statements: 1️⃣ All books are papers. 2️⃣ Some papers are not magazines.<br>Which of the following is logically possible?
medium
A. All books are magazines
B. Some books are magazines
C. No book is a magazine
D. Some books are not magazines

Solution

  1. Step 1: Interpret

    All Books ⊂ Papers; Some Papers are not Magazines ⇒ There exists a section of Papers (and therefore possibly Books) outside Magazines.

  2. Step 2: Derive

    Since Books are part of Papers, it’s possible that some Books fall into the non-Magazine part of Papers.

  3. Final Answer:

    Some books are not magazines. → Option D

  4. Quick Check:

    ‘All + Some not’ ⇒ ‘Some not’ is possible. ✅
Hint: Combine ‘All’ and ‘Some not’ to infer ‘Some not’ about the subset.
Common Mistakes: Assuming ‘All’ overrides partial exclusions from the larger set.
4. Statements: 1️⃣ All flowers are plants. 2️⃣ Some plants are not trees.<br>Which of the following is implied as possible?
medium
A. All flowers are trees
B. Some flowers are trees
C. Some flowers are not trees
D. No flower is a tree

Solution

  1. Step 1: Decode

    All Flowers ⊂ Plants; Some Plants are not Trees ⇒ there exist Plants (and possibly Flowers) outside Trees.

  2. Step 2: Check possible implication

    Since all Flowers are Plants, some of them could belong to that portion of Plants not classified as Trees. So ‘Some Flowers are not Trees’ is possible.

  3. Final Answer:

    Some flowers are not trees. → Option C

  4. Quick Check:

    All subset logic extends exclusions from the parent group. ✅
Hint: Subset + partial exclusion = same exclusion applies to part of subset.
Common Mistakes: Assuming the subset must always share all properties of its superset.
5. Statements: 1️⃣ Some actors are dancers. 2️⃣ Some dancers are not singers.<br>Which of the following can be logically true?
medium
A. All actors are singers
B. Some actors are not singers
C. No actor is a singer
D. Some singers are actors

Solution

  1. Step 1: Understand premises

    Some Actors ↔ Dancers; Some Dancers are not Singers ⇒ Dancers have a section outside Singers.

  2. Step 2: Connect the terms

    Actors who are also Dancers may belong to the non-Singer part of Dancers, making it possible that ‘Some Actors are not Singers.’

  3. Final Answer:

    Some actors are not singers. → Option B

  4. Quick Check:

    ‘Some + Some not’ ⇒ the intersection can exist for the same subgroup. ✅
Hint: When one subset overlaps another that has a ‘Some not’ clause, partial exclusion follows.
Common Mistakes: Assuming overlap means inclusion in all properties (e.g., all dancers are singers).

Mock Test

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