All A's are B's: This means that the set of "A's" is completely contained within the set of "B's". If something is an A, it must necessarily be a B. No B's are C's: This means that the sets of "B's" and "C's" have no intersection; they are completely separate.
If you take any element that is an A, you'll first know that it's a B (by the first rule). But since it's a B, and no B can be a C (by the second rule), then that element cannot be a C.
Logical conclusion: The intersection of A and C is empty.
A) No A's are C's.
No A is C.
Here's the step-by-step reasoning:
All A's are B's: This means that the set of "A's" is completely contained within the set of "B's". If something is an A, it must necessarily be a B.
No B's are C's: This means that the sets of "B's" and "C's" have no intersection; they are completely separate.
If you take any element that is an A, you'll first know that it's a B (by the first rule). But since it's a B, and no B can be a C (by the second rule), then that element cannot be a C.
Logical conclusion: The intersection of A and C is empty.