Negate the conditional statement.

(a∧∼b)⇒∼c

To negate the conditional statement \((a \land \sim b) \Rightarrow \sim c\), we use the logical equivalence that negates an implication:

\[
\sim (P \Rightarrow Q) \equiv P \land \sim Q
\]

Where \(P\) is \((a \land \sim b)\) and \(Q\) is \(\sim c\).

### Step-by-step negation:
1. The negation of the conditional statement \(\sim \left( (a \land \sim b) \Rightarrow \sim c \right)\) is equivalent to:
\[
(a \land \sim b) \land \sim (\sim c)
\]
2. Simplifying \(\sim (\sim c)\) gives \(c\).
   
Thus, the negated form of the statement is:
\[
(a \land \sim b) \land c
\]

This is the final negation of the conditional statement.

Would you like further clarification on any step?

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Here are some related questions:
1. How do you negate a biconditional statement?
2. What is the truth table for the negated statement \((a \land \sim b) \land c\)?
3. Can you provide examples of real-world conditionals and their negations?
4. How does De Morgan's law apply to negating conditionals?
5. What is the relationship between a contrapositive and the negation of a conditional?

**Tip**: When negating conditionals, always break it down into its components and use logical equivalences to simplify step by step.

(a∧∼b)⇒∼c. Negate the conditional statement.

Learn how to negate the conditional statement (a∧∼b)⇒∼c using logical equivalences and step-by-step reasoning. This problem involves key logical concepts such as the negation of an implication and the application of De Morgan's Laws, suitable for advanced high school or undergraduate students.

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