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:
All balls are rackets.
All rackets are bats.
All bats are pads.
Conclusions:
I. No ball is a pad.
II. All bats are rackets.
- ANeither conclusion I nor II follows.
- BOnly conclusion I follows.
- COnly conclusion II follows.
- DBoth conclusions I and II follow.
Solution & Step-by-step Explanation
Let's check each conclusion step by step:
From the statements: Balls⊂Rackets⊂Bats⊂Pads.
This means All balls are pads. Therefore, Conclusion I ("No ball is a pad") is completely false and does not follow.
From the statement "All rackets are bats", we can only conclude that "Some bats are rackets". We cannot definitively say "All bats are rackets". Therefore, Conclusion II does not follow.
Thus, neither conclusion follows.
From the statements: Balls⊂Rackets⊂Bats⊂Pads.
This means All balls are pads. Therefore, Conclusion I ("No ball is a pad") is completely false and does not follow.
From the statement "All rackets are bats", we can only conclude that "Some bats are rackets". We cannot definitively say "All bats are rackets". Therefore, Conclusion II does not follow.
Thus, neither conclusion follows.