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To solve this problem, we need to construct a truth table for the given logical expression:

\[
(\neg p \land q) \rightarrow (p \land \neg q)
\]

Where:
- \(\neg p\) means "not \(p\)" (negation of \(p\)),
- \(\land\) is the logical AND,
- \(\rightarrow\) is the logical implication.

### Steps to Construct the Truth Table:

1. List all possible truth values for \(p\) and \(q\). Since each variable can be either true (T) or false (F), there are 4 possible combinations.
2. Compute the truth values for each sub-expression step by step.
3. Determine whether the statement is a tautology by seeing if the final column is always true.

Here is the truth table layout for the expression:

| \(p\) | \(q\) | \(\neg p\) | \(p \land \neg q\) | \(\neg p \land q\) | \((\neg p \land q) \rightarrow (p \land \neg q)\) |
|:-----:|:-----:|:----------:|:------------------:|:------------------:|:-----------------------------------------------:|
|   T   |   T   |     F      |         F          |         F          |                      T                          |
|   T   |   F   |     F      |         T          |

Construct a truth table for the statement: (~p ∧ q) → (p ∧ ~q). Then determine if the statement is a tautology.

Learn how to construct a truth table for the logical expression (~p ∧ q) → (p ∧ ~q) and determine if the statement is a tautology. This lesson covers propositional logic and logical implication, suitable for students in Grades 9-12.

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