Logic 101 (English)

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Introduction to Logic

Logic Puzzle

If Jack has an A, and all X's are A's, then does Jack definitely have an X?

What we know:

From above we know two facts:
1. Jack has an A (apple)
2. All X's are A's

We would not assume that:

1. All A's are X's
2. Jack's A is an X (red apple)

Logically Why?

Just because all X's are apples does not mean all apples are X's.
We know Jack has an apple, but whether it's an X or not is not clear. Since we would be wrong to assume all apples are X's, then we might be wrong to assume Jack's apple is an X. That's not to say we know Jack's apple is not an X. The truth is, we don't have enough information to determine if Jack's apple is an X or not.

Solving Logic Puzzle 

Consider what if X stood for a red apple. Then we know Jack has an apple; we know all red apples are apples. But we don't know if Jack's apple is red or not. We simply weren't given enough information.

So when asked if Jack has an X or not, the correct answer is that we don't know or just no, if no better choice is presented. The answer no requires explanation, which is that we don't have enough information.

However, since the question asks if Jack definitely has an apple, meaning 100% certainty, then the answer is no, regardless of what color apple Jack might have. The reason for this is that the word definitely changes the question from asking if Jack's apple is also red to ask if the percent chance of him having a red apple is certainly 100%; so, the meaning of the question has changed from a question that does not provide enough information to a question that requires a numeric calculation to determine the percent value and establish a true or false response.

Logic Puzzle Solution

Therefore, while Jack may indeed have a red apple, the percent chance of him having a red apple is not 100%. In other words, he might have a red apple, or he might have a green apple, but we were not given enough information in the two facts that we know in order to determine the color of his apple. So, therefore, the percent chance of him having a red apple is relative to other color apples he might have, such as green. Based on the two facts that we know, we cannot assume all apples are X's. That would be like saying all apples are red, which we know is not true.

Logic Puzzle Answer

So, does Jack definitely have an X?

Absolutely not.

Maybe he does, but that doesn't answer the question being asked.