In the question given below, three statements are followed by two conclusions numbered (I) and (II). You have to take the given statements to be true. Read the conclusions and given the answer. Statements : Some symbols are figures. All symbols are graphics. No graphic is a picture. Conclusions : (I) Some graphics are figures. (II) Some symbols are pictures.
- (1)Neither Conclusion (I) nor Conclusion (II) follows.
- (2)Both Conclusion (I) and (II) follow.
- (3)Only Conclusion (I) follows.
- (4)Only Conclusion (II) follows.
Answer
Why
Correct — option (3), Only Conclusion (I) follows.
Take all three statements as true and test each conclusion against them.
Conclusion (I), "Some graphics are figures":
Step 1 — "Some symbols are figures": at least one symbol is also a figure.
Step 2 — "All symbols are graphics": that symbol is a graphic as well.
Step 3 — so at least one graphic is a figure. (I) follows.
Conclusion (II), "Some symbols are pictures":
Step 1 — "All symbols are graphics".
Step 2 — "No graphic is a picture".
Step 3 — so no symbol is a picture. (II) says the opposite, so it does not follow.
One conclusion follows and one does not: Only Conclusion (I) follows.
The idea to remember: "All A are B" with "No B is C" gives "No A is C" — everything inside B is shut out of C.
Why the others are wrong
- (1)Neither Conclusion (I) nor Conclusion (II) follows. — Option (1) rejects conclusion (I), which the statements force.
The symbols that are figures are, like every symbol, graphics. So at least one graphic is a figure. The link between graphics and figures is not stated directly; it runs through symbols. This option would be right only if (I) could fail in some diagram, and it cannot.
- (2)Both Conclusion (I) and (II) follow. — Option (2) accepts conclusion (II), which the statements rule out.
Every symbol is a graphic, and no graphic is a picture, so no symbol is a picture. "Some symbols are pictures" is the contradiction of that result, not just an unproven claim.
- (4)Only Conclusion (II) follows. — Option (4) gets both conclusions backwards.
It rejects (I), which follows because the symbols that are figures are graphics. It accepts (II), which fails because all symbols are graphics and no graphic is a picture, so no symbol can be a picture.
Concept
A categorical statement links two classes in one of four forms: All A are B, No A is B, Some A are B, and Some A are not B. "Some" means at least one, and possibly all.
Statements can be chained through a shared class. All A are B with All B are C gives All A are C. All A are B with No B is C gives No A is C. Some A are B with All B are C gives Some A are C.
"Some A are B" and "No A is B" can be reversed. "All A are B" cannot: it gives only "Some B are A".
RPSC's 2024 syllabus lists "Statements and Conclusion" under "Logical Reasoning (Deductive, Inductive, Abductive)" in Reasoning & Mental Ability.
A syllogism is deductive reasoning. If the premises are true and the form is valid, the conclusion must be true; nothing outside the premises is used. Inductive reasoning, by contrast, generalises from cases and gives a probable conclusion.
The categorical syllogism, with its all, no and some statements, goes back to Aristotle's logic. Venn diagrams give a visual check: a conclusion follows only if it holds in every diagram that fits the statements.
Key facts
- All symbols are graphics + No graphic is a picture → No symbol is a picture.
- Some symbols are figures + All symbols are graphics → Some graphics are figures.
- "Some A are B" reverses to "Some B are A"; "No A is B" reverses to "No B is A".
- "All A are B" does not reverse to "All B are A"; it yields only "Some B are A".
- A conclusion follows only if it is true in every Venn diagram consistent with the statements.
(I) links graphics and figures through symbols; (II) links symbols and pictures through graphics.
Study next
Common traps
- No statement links graphics and figures directly. Conclusion (I) still follows, because the link runs through symbols.
- "All symbols are graphics" does not mean "All graphics are symbols". Graphics may exist that are neither symbols nor figures.
- "Some symbols are figures" does not say some symbols are not figures. "Some" means at least one, and can include all.
A question can give two, three or four statements using all, some and no, followed by two or more conclusions, as this one does.
A question can also add "some… not" statements, test possibility conclusions such as "all X can be Y", pair conclusions of which one must be true, or ask which statements lead to a given conclusion.
Related PYQs
UnlockIAS will link similar questions from RAS Pre 2018 and 2016 here once those papers are published on this site.
Practice
- practice — not a real PYQ
Statements: All pens are tools. Some tools are gifts. No gift is cheap. Conclusions: (I) Some pens are gifts. (II) Some tools are not cheap.
- (a)Neither Conclusion (I) nor Conclusion (II) follows.
- (b)Both Conclusion (I) and (II) follow.
- (c)Only Conclusion (I) follows.
- (d)Only Conclusion (II) follows.
Answer(4) — (II): the tools that are gifts cannot be cheap, because no gift is cheap, so some tools are not cheap. (I): the tools that are gifts need not be pens, so "some pens are gifts" is not certain. Option (1) rejects (II); options (2) and (3) accept (I). - practice — not a real PYQ
Statements: All notes are paper. No coin is paper. Conclusions: (I) No note is a coin. (II) Some papers are notes.
- (a)Neither Conclusion (I) nor Conclusion (II) follows.
- (b)Both Conclusion (I) and (II) follow.
- (c)Only Conclusion (I) follows.
- (d)Only Conclusion (II) follows.
Answer(2) — (I): every note is paper and no paper is a coin (reversing "No coin is paper"), so no note is a coin. (II): "All notes are paper" yields "Some papers are notes". Both follow, so options (1), (3) and (4) each reject at least one valid conclusion.