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The image shows a partial truth table for the logical statement \((p \lor q) \rightarrow (\neg r \rightarrow \neg q)\). I'll complete the table and ensure that it is correct.

Here's the step-by-step breakdown of how to approach this truth table:

### Logical Statements:
- \(p \lor q\): "p OR q" (true if either \(p\) or \(q\) is true).
- \(\neg r \rightarrow \neg q\): "if not r, then not q" (a conditional that is false only if \(\neg r\) is true and \(\neg q\) is false).
- \((p \lor q) \rightarrow (\neg r \rightarrow \neg q)\): This is a conditional that we're evaluating in the last column.

The table should cover all combinations of truth values for \(p\), \(q\), and \(r\), then we'll evaluate the intermediate columns.

I'll start by filling in the missing parts. Would you like the table completed, or would you prefer a step-by-step breakdown on how to fill each column?

The user submitted a truth table problem for the logical statement (p ∨ q) → (¬r → ¬q).

Understand how to complete the truth table for the logical statement (p ∨ q) → (¬r → ¬q). This detailed breakdown includes logical operators such as disjunction, negation, and implication. Suitable for students in discrete mathematics courses.

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