Negate the conditional statement.

(∼a∧b)⇒c

To negate the conditional statement \((∼a∧b)⇒c\), we can use the logical equivalence:

\[
\neg(p \Rightarrow q) \equiv p \land \neg q
\]

In this case, \( p = (∼a ∧ b) \) and \( q = c \). Using the rule above:

\[
\neg((∼a ∧ b) \Rightarrow c) \equiv (∼a ∧ b) ∧ \neg c
\]

Thus, the negation of \((∼a ∧ b) \Rightarrow c\) is:

\[
(∼a ∧ b) ∧ ∼c
\]

Would you like more details on this process or any further explanation?

Here are 5 related questions:
1. How do you negate other forms of conditionals, like \( p \Rightarrow q \)?
2. What is the contrapositive of a conditional statement?
3. How does De Morgan's Law apply to conjunctions and disjunctions?
4. What is the difference between implication and biconditional statements?
5. How do you simplify expressions involving multiple negations?

**Tip**: Negating a conditional statement often results in a conjunction of the hypothesis and the negation of the conclusion.

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

Understand how to negate the conditional statement (∼a ∧ b) ⇒ c using logical equivalence rules. This solution demonstrates the use of propositional logic and negation principles to transform the statement into (∼a ∧ b) ∧ ¬c. Ideal for students studying logic at the high school level (Grades 11-12).

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