Thinking...
Okay, so the question is: If all A are B and all B are C, are all A
definitely C? And the options are Yes or No, then explain in one sentence.
Hmm, let me think.
First, I need to remember the logical structure here. The problem states tw
two conditions: all A are B, meaning that if something is A, it must be B.
And all B are C, meaning if something is B, it must be C. The question is a
asking if all A are definitely C. So, does the second condition imply that
all A are C?
Let me break it down. If all A are B, then every A is B. And all B are C, s
so every B is C. So, combining these two, does that mean every A is C? Let
me think of an example. Suppose A is a set, B is a subset, and C is another
another subset. Then if A is a subset of B and B is a subset of C, then A i
is a subset of C. So yes, in that case, all A are C.
But wait, is there a possibility that A is a subset of B, but B is not a su
subset of C? No, because the problem says all B are C, meaning that every B
B is C. So if B is a subset of C, then A is a subset of B, which is a
subset of C. So yes, all A must be C. Therefore, the answer should be Yes.
But maybe I should check with another example. Suppose A is a group, B is a
a set within A, and C is a set within B. Wait, no, all B are C means that a
any element in B must be in C. But A is a subset of B, so A is a subset of
C. So yes. So the conclusion is Yes.
Therefore, the answer should be Yes, and the explanation is that if all A a
are B and all B are C, then all A are definitely C because every element of
of A is in B, and every element of B is in C, making every element of A in
C.
So the one-sentence answer would be: Yes, all A are definitely C because al
all A are B and all B are C, so every A is C.
...done thinking.
Yes, all A definitely C because if all A are B and all B are C, then every
A must also be C.
**Explanation:** The logical structure is that A ⊂ B and B ⊂ C, so
combining these implies A ⊂ C.