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.