Question

Given that this statement is true, I will go on the Internet if and only if I can watch a movie, then the statement I go on the Internet and I cannot watch a movie is true.


True

False

Answer 1

The statement "I will go on the Internet if and only if I can watch a movie" can be expressed in logical terms as follows:

Let:
- \( P \): "I go on the Internet"
- \( Q \): "I can watch a movie"

The original statement means that:
- \( P \) is true if and only if \( Q \) is true (\( P \iff Q \)).

This implies two conditions:
1. If I go on the Internet (\( P \) is true), then I can watch a movie (\( Q \) is true).
2. If I cannot watch a movie (\( Q \) is false), then I do not go on the Internet (\( P \) is false).

Now, consider the statement: "I go on the Internet and I cannot watch a movie." This can be expressed as:
- \( P \) is true and \( Q \) is false (\( P \land \neg Q \)).

If \( Q \) is false, then according to the original statement (\( P \iff Q \)), \( P \) must also be false. This means that it is not possible for \( P \) to be true while \( Q \) is false.

Therefore, the statement "I go on the Internet and I cannot watch a movie" cannot be true, as it contradicts the original condition.

So, the answer is **False**.