The logical expression in the image is:

$\neg (q \Rightarrow \neg p) \Rightarrow (\neg p \lor q)$

Let’s break it down and simplify:

Step 1: Rewrite the implications using logical equivalences.

The implication $q \Rightarrow \neg p$ can be rewritten as: $q \Rightarrow \neg p \equiv \neg q \lor \neg p$ So the expression becomes: $\neg (\neg q \lor \neg p) \Rightarrow (\neg p \lor q)$

Step 2: Apply De Morgan's law to the negation.

De Morgan's law tells us that: $\neg (\neg q \lor \neg p) \equiv q \land p$ Now the expression is: $(q \land p) \Rightarrow (\neg p \lor q)$

Step 3: Analyze the implication.

The expression $(q \land p) \Rightarrow (\neg p \lor q)$ holds true because:

• $q \land p$ implies both $q$ and $p$ are true.
• The right side $\neg p \lor q$ will be true because either $q$ is true (which it is if $q \land p$ holds) or $\neg p$ is true (which doesn't need to hold if $q$ is already true).

Thus, this expression is a tautology (always true).

Let me know if you'd like a further breakdown or explanation of any step!

Here are 5 related questions that may help you deepen your understanding:

1. How does De Morgan's law work in logical expressions?
2. What other equivalent transformations are possible in propositional logic?
3. Can you provide an example where $q \land p$ is false, and verify if the implication still holds?
4. What are the truth table results for this expression?
5. How does implication ($\Rightarrow$) relate to disjunction ($\lor$) in logic?

Tip: Always convert implications to disjunctions in order to simplify complex logical expressions.