Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some lamps are bulbs.
All bulbs are tubes.
Some tubes are pipes.
Conclusions:
I. All bulbs are pipes.
II. At least some lamps are tubes.
- ANeither conclusion I nor II follows
- BOnly conclusion II follows
- CBoth conclusions I and II follow
- DOnly conclusion I follows
Solution & Step-by-step Explanation
Let's evaluate using Venn diagrams or logical relations:
Statements:
Some lamps are bulbs.
All bulbs are tubes.
Since all bulbs are tubes and some lamps are bulbs, it means the portion of lamps that are bulbs will definitely be tubes. Thus, "Some lamps are tubes" is definitely true.
Some tubes are pipes.
Conclusions:
I. All bulbs are pipes: No direct relation is given between bulbs and pipes. They may or may not overlap. Therefore, this is not a definite conclusion. (Does not follow)
II. At least some lamps are tubes: As established from statements 1 and 2, the intersection of lamps and bulbs is entirely inside tubes, so some lamps are definitely tubes. (Follows)
Hence, only conclusion II follows.
Statements:
Some lamps are bulbs.
All bulbs are tubes.
Since all bulbs are tubes and some lamps are bulbs, it means the portion of lamps that are bulbs will definitely be tubes. Thus, "Some lamps are tubes" is definitely true.
Some tubes are pipes.
Conclusions:
I. All bulbs are pipes: No direct relation is given between bulbs and pipes. They may or may not overlap. Therefore, this is not a definite conclusion. (Does not follow)
II. At least some lamps are tubes: As established from statements 1 and 2, the intersection of lamps and bulbs is entirely inside tubes, so some lamps are definitely tubes. (Follows)
Hence, only conclusion II follows.