Easy
syllogismlogicdeductive-reasoning
If all A are B and some B are C, are all A necessarily C?
Problem Statement
Consider the following logical statements:
1. All A are B.
2. Some B are C.
Based only on these premises, can we logically conclude that all A are C?
Answer
No, it does not necessarily follow that all A are C.
Step-by-Step Explanation
- 1
The statement 'All A are B' tells us that every member of set A is contained within set B.
- 2
The statement 'Some B are C' means that at least one element in set B is also in set C.
- 3
However, we are not told which elements of B are in C.
- 4
It is entirely possible that the B elements that belong to A are not the same B elements that belong to C.
- 5
Because of this uncertainty, we cannot logically conclude that all A are C.