The logical expression in the image is:

$\neg q \vee ((p \land \neg r) \vee (p \land \neg q))$

This is a propositional logic expression, where:

• $\neg$ represents logical negation (NOT),
• $\vee$ represents logical disjunction (OR),
• $\land$ represents logical conjunction (AND).

Let me simplify the expression step by step:

1. Start with the expression: $\neg q \vee ((p \land \neg r) \vee (p \land \neg q))$

2. Apply distribution to combine similar terms inside the second part of the disjunction: $(p \land \neg r) \vee (p \land \neg q)$ This can be factored using the distributive property: $p \land (\neg r \vee \neg q)$

3. The entire expression now becomes: $\neg q \vee (p \land (\neg r \vee \neg q))$

4. Distribute $\neg q$ over the expression to see if there's further simplification: $\neg q \vee p$

This is the simplified form of the given logical expression.

Would you like more details or clarification? Here are a few questions you might consider:

1. How do you factor expressions in propositional logic?
2. What is the distributive property in logic?
3. What is the difference between $\vee$ (OR) and $\land$ (AND)?
4. How do logical identities help simplify expressions?
5. What is the significance of logical negation $\neg$?

Tip: When simplifying complex logical expressions, try using the distributive property or De Morgan’s laws for quick reductions.