Two statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All clothes are black.
All shirts are clothes.
Conclusions:
I. All shirts are black.
II. Some clothes are black.
- ANeither conclusion I nor conclusion II follows
- BBoth conclusions I and II follow
- COnly conclusion I follows
- DOnly conclusion II follows
Solution & Step-by-step Explanation
Let's analyze the statements using a Venn diagram approach:
Statement 2 says "All shirts are clothes." This means the set of 'Shirts' is entirely contained inside the set of 'Clothes'.
Statement 1 says "All clothes are black." This means the set of 'Clothes' is entirely contained inside the set of 'Black'.
Now let's evaluate the conclusions:
Conclusion I: "All shirts are black." Since 'Shirts' is inside 'Clothes', and 'Clothes' is inside 'Black', 'Shirts' must be inside 'Black'. Therefore, conclusion I definitely follows.
Conclusion II: "Some clothes are black." Since "All clothes are black" is true, any subset of clothes must also be black. In logic, if 'All' is true, its sub-implication 'Some' is also true. Therefore, conclusion II follows.
Both conclusions I and II follow.
Statement 2 says "All shirts are clothes." This means the set of 'Shirts' is entirely contained inside the set of 'Clothes'.
Statement 1 says "All clothes are black." This means the set of 'Clothes' is entirely contained inside the set of 'Black'.
Now let's evaluate the conclusions:
Conclusion I: "All shirts are black." Since 'Shirts' is inside 'Clothes', and 'Clothes' is inside 'Black', 'Shirts' must be inside 'Black'. Therefore, conclusion I definitely follows.
Conclusion II: "Some clothes are black." Since "All clothes are black" is true, any subset of clothes must also be black. In logic, if 'All' is true, its sub-implication 'Some' is also true. Therefore, conclusion II follows.
Both conclusions I and II follow.