Premises: All apples are golden in colour. No golden coloured things are cheap.
Conclusions:
- I. All apples are cheap.
- II. Golden coloured apples are not cheap.
Which of the following conclusions follow logically?
Only I
Only II
Both I and II
Neither I nor II
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CAPF – 2015
From premise (1), we know that the set of apples is a subset of golden coloured things. From premise (2), we know that the set of golden coloured things and the set of cheap things have no overlap.
Combining these, since all apples are golden coloured, and no golden coloured things are cheap, it follows that no apples are cheap.
Conclusion I states: “All apples are cheap.” This is directly contradicted by the logical consequence of the premises (“No apples are cheap”). Thus, Conclusion I does not follow.
Conclusion II states: “Golden coloured apples are not cheap.” Apples that are golden coloured are, by definition, golden coloured things. According to premise (2), no golden coloured things are cheap. Therefore, golden coloured apples are not cheap. This conclusion follows directly from the premises.
Premise 1: All A are G.
Premise 2: No G are C. This implies No C are G, and if something is G, it is not C.
Conclusion I: All A are C. (False)
Conclusion II: Apples that are G are not C. Since all A are G, this is equivalent to saying A are not C. From “All A are G” and “No G are C”, we deduce “No A are C” (which means A are not C). Therefore, Conclusion II follows.