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Possibility & Either-Or Cases

General Intelligence & Reasoning · Syllogism

Useful for: SSC CGL

Overview

Possibility conclusions ask whether something can be true in at least one valid diagram; either–or applies to complementary pairs that cannot both be definite.

Key points

A possibility follows if it does not contradict any statement.
A possibility does not follow if a definite "No" or "All" already rules it out.
Either–or: a pair like "Some A are C" / "No A is C" where neither follows definitely and together they cover all cases.
"All A being C is a possibility" follows when nothing restricts A from lying fully inside C.
Definite conclusions always beat possibilities.

Explanation

If a statement says "No B is C" and all A are B, then "Some A being C is a possibility" does not follow.
Check possibilities by redrawing circles, not by intuition.
Either–or pairs must have the same subject and predicate.
Some + Some: many possibilities exist; check each against the statements.

Step by step

Draw the definite case.
Try an alternative diagram.
Decide possible or not.

Examples

All cats are dogs; no dog is a rat. "Some cats being rats is a possibility" does not follow (no cat is a rat definitely).
Some books are pens; some pens are bags. "All books being bags is a possibility" follows (no statement forbids it).
Some A are C (not definite) and No A is C (not definite) → either–or follows.

Traps and advanced points

Trap: Calling a possibility "definite".
Trap: Accepting a possibility that contradicts a "No" statement.
Trap: Using either–or for a non-complementary pair.

Quick revision

Possible = not contradicted.
Definite conclusions rule out possibilities.
Either–or needs a complementary pair.

Practice MCQs

Statements: Some A are B. Conclusions: I. Some B are A. II. All A are B. Which follows?
1. Only I follows
2. Only II follows
3. Both follow
4. Neither
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Answer: (a) Only I follows. 'Some A are B' ka conversion → 'Some B are A' (I) hamesha follows.
Statements: All P are Q. Conclusions: I. Some Q are P. II. No P is Q. Which follows?
1. Only I follows
2. Only II follows
3. Both
4. Neither
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Answer: (a) Only I follows. 'All P are Q' → 'Some Q are P' (I) follows (conversion).
Which pair forms a complementary (Either-Or) case?
1. No A is B & No B is A
2. All A are B & All B are A
3. Some A are B & No A is B
4. All A are B & Some A are B
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Answer: (c) Some A are B & No A is B. Either-Or tab banta jab do conclusions same subject-predicate ke saath complementary hon (ek positive, ek negative).
Statements: Some books are pens. All pens are red. Conclusion: Some books being red is a possibility.
1. Does not follow
2. Either or
3. False
4. Follows (it's definite, so possibility holds)
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Answer: (d) Follows (it's definite, so possibility holds). Some books are pens, all pens red → wo books jo pens hain, red hain (definite).
Statements: No cat is dog. All dogs are pets. Conclusion I: Some pets are not cats. II: No cat is pet.
1. Only I follows
2. Only II follows
3. Both
4. Neither
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Answer: (a) Only I follows. All dogs are pets, no cat is dog → wo pets jo dogs hain, cats nahi (Some pets are not cats = I follows).
Statements: All roses are flowers. Some flowers fade quickly. Conclusion: Some roses fade quickly.
1. Follows
2. Definitely
3. Either or
4. Does not follow
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Answer: (d) Does not follow. All roses are flowers, but 'some flowers fade' — ye fading flowers roses waale group se overlap karein zaroori nahi.
Statements: Some X are Y. All Y are Z. Conclusions: I. Some X are Z. II. Some Z are X.
1. Both follow
2. Only I
3. Only II
4. Neither
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Answer: (a) Both follow. Some X are Y, all Y are Z → wo X jo Y hain, Z bhi hain (Some X are Z = I).
Statements: No A is B. Conclusion: No B is A. This is an example of:
1. Either or
2. Possibility
3. Valid conversion
4. Invalid
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Answer: (c) Valid conversion. 'No A is B' ka conversion 'No B is A' hamesha valid hai (E-type statement symmetric hai).
Statements: Some students are toppers. No topper is lazy. Conclusion: Some students are not lazy.
1. None
2. Follows
3. Does not follow
4. Either or
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Answer: (b) Follows. Some students are toppers; no topper is lazy → wo students jo toppers hain, lazy nahi.
In syllogism, if both conclusions individually do not follow but together cover all possibilities, the answer is:
1. Either I or II follows
2. Both follow
3. Neither follows
4. Only I follows
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Answer: (a) Either I or II follows. Jab dono individually na follow karein par complementary hokar saari possibilities cover karein → 'Either I or II follows'.
All engineers are learners. Some engineers are experienced. Which conclusion definitely follows?
1. Some experienced people are learners
2. All learners are engineers
3. All experienced people are engineers
4. No engineers are experienced
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Answer: (a) Some experienced people are learners. If some A are experienced and all A are B, then some experienced are B.
All researchers are trained people. Some researchers are urban. Which conclusion definitely follows?
1. No researchers are urban
2. All trained people are researchers
3. All urban people are researchers
4. Some urban people are trained people
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Answer: (d) Some urban people are trained people. If some A are urban and all A are B, then some urban are B.
All chefs are volunteers. Some chefs are urban. Which conclusion definitely follows?
1. All volunteers are chefs
2. No chefs are urban
3. All urban people are chefs
4. Some urban people are volunteers
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Answer: (d) Some urban people are volunteers. If some A are urban and all A are B, then some urban are B.
All farmers are graduates. Some farmers are experienced. Which conclusion definitely follows?
1. All graduates are farmers
2. All experienced people are farmers
3. Some experienced people are graduates
4. No farmers are experienced
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Answer: (c) Some experienced people are graduates. If some A are experienced and all A are B, then some experienced are B.
All teachers are citizens. Some teachers are experienced. Which conclusion definitely follows?
1. All experienced people are teachers
2. No teachers are experienced
3. All citizens are teachers
4. Some experienced people are citizens
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Answer: (d) Some experienced people are citizens. If some A are experienced and all A are B, then some experienced are B.