When solving for simple math problems I constantly encounter the output does not render correctly.
ChatGPT does it:
My local app does it:
Even my user question made pretty:
What have you got there that doesn’t do it?
Perhaps a better look at the inline and block LaTeX containers to be handled by MathJax or such would help you out?
### 1. **Apply De Morgan’s Law to the negations**
#### Expression 1: \(\neg(\neg P(x) \lor Q(x))\)
Using De Morgan's laws:
\[
\neg(A \lor B) \equiv \neg A \land \neg B
\]
Let \(A = \neg P(x)\) and \(B = Q(x)\). Applying the law:
\[
\neg(\neg P(x) \lor Q(x)) \equiv \neg(\neg P(x)) \land \neg(Q(x))
\]
Simplify the double negation:
\[
\neg(\neg P(x) \lor Q(x)) \equiv P(x) \land \neg Q(x)
\]
#### Expression 2: \(\neg(\neg Q(x) \lor P(x))\)
Similarly, using De Morgan's laws:
\[
\neg(A \lor B) \equiv \neg A \land \neg B
\]
Let \(A = \neg Q(x)\) and \(B = P(x)\). Applying the law:
\[
\neg(\neg Q(x) \lor P(x)) \equiv \neg(\neg Q(x)) \land \neg(P(x))
\]
Simplify the double negation:
\[
\neg(\neg Q(x) \lor P(x)) \equiv Q(x) \land \neg P(x)
\]
### 2. **Interpret the negations**
#### Given interpretations:
- \(\neg P(x)\): \(x\) is even.
- \(\neg Q(x)\): \(x^2\) is even.
From these, we can deduce:
- \(P(x)\): \(x\) is odd (negation of \(\neg P(x)\)).
- \(Q(x)\): \(x^2\) is odd (negation of \(\neg Q(x)\)).
#### Interpretation of Expression 1: \(P(x) \land \neg Q(x)\)
- \(P(x)\): \(x\) is odd.
- \(\neg Q(x)\): \(x^2\) is even.
Thus, \(P(x) \land \neg Q(x)\) means:
- \(x\) is odd, and \(x^2\) is even.
This is a contradiction because if \(x\) is odd, then \(x^2\) must also be odd. Therefore, this expression is **unsatisfiable** (it cannot be true for any \(x\)).
#### Interpretation of Expression 2: \(Q(x) \land \neg P(x)\)
- \(Q(x)\): \(x^2\) is odd.
- \(\neg P(x)\): \(x\) is even.
Thus, \(Q(x) \land \neg P(x)\) means:
- \(x\) is even, and \(x^2\) is odd.
This is also a contradiction because if \(x\) is even, then \(x^2\) must also be even. Therefore, this expression is **unsatisfiable** (it cannot be true for any \(x\)).
### Final Conclusion:
Both expressions, when interpreted in terms of whether \(x\) or \(x^2\) is even or odd, are logically **unsatisfiable**.
You also have to make sure that Markdown doesn’t damage the LaTeX or vice versa.
Then this is likely a AI model quality issue with ChatGPT, it not producing post-trained sequences that align it with the ChatGPT web renderer.
You can note the model name and type currently being used, even share a chat here, but the developer forum, where fellow users can help with coding AI products, is not the primary support mechanism for reporting ChatGPT quality issues.
You can express your dislike of a bad ChatGPT output by pressing the “thumbs-down” feedback button in the user interface. Regenerate the response until you get one that hasn’t made mistakes.
