If All A are B, and All B are C, then All A are C. True or False?

If All A are B, and All B are C, then All A are C. True or False?

• A. True
• B. False
• C. Both may be true
• D. Neither statement can be determined

Answer: (A)

The main idea here is how containment works in a chain of categories. If every A is a B, and every B is a C, then every A is a C. This follows because any object that is in A is automatically in B, and any object in B is automatically in C. So that object must be in C as well. A quick check helps: take any A and you can follow this path—A implies B, and B implies C—so A implies C. For example, all apples are fruits, all fruits are edible, therefore all apples are edible. The statement is true because the relationship is transitive across these categories.

The main idea here is how containment works in a chain of categories. If every A is a B, and every B is a C, then every A is a C. This follows because any object that is in A is automatically in B, and any object in B is automatically in C. So that object must be in C as well. A quick check helps: take any A and you can follow this path—A implies B, and B implies C—so A implies C. For example, all apples are fruits, all fruits are edible, therefore all apples are edible. The statement is true because the relationship is transitive across these categories.