Use De Morgan's Laws to write an equivalent statement without using parentheses.

∼(∼p∧∼q)

To use De Morgan's Laws to rewrite the statement \(\sim (\sim p \land \sim q)\) without using parentheses, we proceed as follows:

1. Apply De Morgan's Law: \(\sim (\sim p \land \sim q)\) becomes \(\sim (\sim p) \lor \sim (\sim q)\).
2. Simplify the double negations: \(\sim (\sim p)\) is equivalent to \(p\), and \(\sim (\sim q)\) is equivalent to \(q\).

Thus, the equivalent statement is:

\[ p \lor q \]

Would you like more details or have any questions? Here are 5 related questions:

1. What is De Morgan's Law for negating a disjunction?
2. How would you negate the statement \(\sim (p \lor q)\)?
3. Can you apply De Morgan's Laws to the statement \(\sim (p \lor (q \land r))\)?
4. How do De Morgan's Laws relate to the rules of distribution in logic?
5. How would you express \( \sim (p \land q \land r) \) using De Morgan's Laws?

**Tip:** De Morgan's Laws are very useful in simplifying complex logical expressions and making them easier to work with in both mathematical proofs and programming.

Use De Morgan's Laws to write an equivalent statement without using parentheses. ∼(∼p∧∼q)

Learn how to apply De Morgan's Laws to simplify the logical expression ∼(∼p∧∼q). This solution involves understanding negation and logical conjunctions, making it suitable for high school students in Grades 9-12.

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