Two statements are given below followed by two conclusions numbered (1) and (2). Take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the

Question

Two statements are given below followed by two conclusions numbered (1) and (2). Take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.

Statements: Some mangoes are yellow. Some fruits are mangoes.

Conclusions:
1. Some mangoes are green.
2. Fruits are yellow.

Give answer:
(A) If only conclusion (1) follows.
(B) If only conclusion (2) follows.
(C) If either (1) or (2) follows.
(D) If neither (1) nor (2) follows.
(E) If both (1) and (2) follow.

Accepted Answer

> [!TLDR] "Some mangoes are yellow" and "Some fruits are mangoes" are two particular (I-type) statements with no distributed middle term, so no valid conclusion linking fruits and yellow (or introducing green) can be drawn — neither conclusion follows.

> [!FORMULA]
> **Syllogism rule (Some + Some = No valid conclusion):** two particular affirmative statements, "Some $A$ are $B$" and "Some $C$ are $A$", share a common term $A$, but since $A$ is NOT distributed in either premise, no definite conclusion about the relation between $B$ and $C$ can be drawn.
> Here: mangoes = $A$, yellow = $B$ ("Some $A$ are $B$"), fruits = $C$ ("Some $C$ are $A$").

1. Statement 1: Some $A$ are $B$ ("Some mangoes are yellow") — only PART of the mangoes are known to be yellow.
2. Statement 2: Some $C$ are $A$ ("Some fruits are mangoes") — only PART of the fruits are known to be mangoes, and it is not guaranteed these are the SAME mangoes that are yellow. …

Connective	Symbol	Reads as	New statement is true when…
Negation	$\neg$	not	The original is false
Conjunction	$\land$	and	Both are true
Disjunction	$\lor$	or	At least one is true
Conditional	$\to$	if…then	The first is false OR the second is true
Biconditional	$\leftrightarrow$	if and only if	Both have the same truth value

Q.Two statements are given below followed by two conclusions numbered

Concept understanding — Creating New Statements

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Why This Matters

Q.Two statements are given below followed by two conclusions numbered

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