Thinking...
The user asks: "If all A are B and all B are C, are all A definitely C? Yes
Yes or No, then explain in one sentence."
We need to answer with a yes/no and then an explanation in one sentence.
The logical statement: If all A are B (A ⊆ B) and all B are C (B ⊆ C), then
then by transitivity, all A are C. So the answer is Yes. Then we need to ex
explain in one sentence. Something like "Yes, because if every member of se
set A belongs to set B and every member of set B belongs to set C, then
each member of A must also belong to set C." That's a single sentence?
Actually that's two clauses but it's one sentence: "Yes, because if every m
member of set A belongs to set B and every member of set B belongs to set C
C, then each member of A necessarily belongs to set C." That is one
sentence. So answer: Yes; because ... That would be a single sentence? The
instruction: "Yes or No, then explain in one sentence." Possibly they want
something like:
"Yes; all members of A are subsets of B and all members of B are subsets of
of C, so every member of A is also a member of C."
That's two sentences. But they said "then explain in one sentence." So
maybe combine: "Yes; because if every A is B and every B is C, then all A m
must be C." That's still one sentence? Actually it's a semicolon, but it's
still one sentence (two independent clauses separated by semicolon). That c
could count as one sentence. Or we can do: "Yes, since any element of A is
also an element of B and any element of B is also an element of C, all A ar
are necessarily C." That's one sentence.
Thus answer: Yes, since any element of A is also an element of B and any el
element of B is also an element of C, all A are necessarily C. That's a
single sentence? It has a semicolon but it's still one sentence. So we can
do that.
Thus final answer:
Yes, since any element of A is also an element of B and any element of B is
is also an element of C, all A are necessarily C.
...done thinking.
Yes, since any element of A is also an element of B and any element of B is
is also an element of C, all A are necessarily C.