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:
Some pants are shirts.
No shirt is a tie.
Conclusions:
I. All pants can never be ties.
II. All ties are pants.
- AOnly conclusion II follows
- BNeither conclusion I nor II follows
- CBoth conclusions I and II follow
- DOnly conclusion I follows
Solution & Step-by-step Explanation
Let's interpret the statements using set intersections:
"Some pants are shirts" means there is a common region between Pants and Shirts (Pants∩Shirts
=∅).
"No shirt is a tie" means the set of Shirts and Ties are completely disjoint (Shirts∩Ties=∅).
Now evaluating conclusions:
Conclusion I: "All pants can never be ties." The portion of pants that are inside shirts can never cross over to enter the tie circle because no shirt can be a tie. Therefore, it is impossible for all pants to ever become ties. This conclusion is absolutely correct and follows.
Conclusion II: "All ties are pants." There is no direct affirmative statement or requirement making ties completely a subset of pants. This does not follow.
Hence, only conclusion I follows.
"Some pants are shirts" means there is a common region between Pants and Shirts (Pants∩Shirts
=∅).
"No shirt is a tie" means the set of Shirts and Ties are completely disjoint (Shirts∩Ties=∅).
Now evaluating conclusions:
Conclusion I: "All pants can never be ties." The portion of pants that are inside shirts can never cross over to enter the tie circle because no shirt can be a tie. Therefore, it is impossible for all pants to ever become ties. This conclusion is absolutely correct and follows.
Conclusion II: "All ties are pants." There is no direct affirmative statement or requirement making ties completely a subset of pants. This does not follow.
Hence, only conclusion I follows.