StatementsSome birds are parrots.All parrots are black.No black is a white.Some whites are birds.Conclusions1. Some birds which are black are not white.2. All parrots which are black are necessarily birds.
Question
StatementsSome birds are parrots.All parrots are black.No black is a white.Some whites are birds.Conclusions1. Some birds which are black are not white.2. All parrots which are black are necessarily birds.
Solution
Let's analyze the statements and conclusions one by one:
Statements:
- Some birds are parrots.
- All parrots are black.
- No black is a white.
- Some whites are birds.
Conclusions:
- Some birds which are black are not white.
- All parrots which are black are necessarily birds.
Step by Step Analysis:
- From the first statement, we know that there are some birds which are parrots.
- From the second statement, we know that all parrots are black.
- Combining these two, we can conclude that there are some birds which are black (since some birds are parrots and all parrots are black).
- From the third statement, we know that no black is a white. So, the birds which are black cannot be white. Hence, the first conclusion "Some birds which are black are not white" is true.
- From the second statement, we know that all parrots are black. And from the first statement, we know that some birds are parrots. So, all parrots which are black are necessarily birds. Hence, the second conclusion "All parrots which are black are necessarily birds" is also true.
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