Use De Morgans Laws to write an equivalent statement for the given sentence. It is false that the band plays rock music or the band has a guitarist

We will apply **De Morgan's Laws** to rewrite the given statement.

### Original Statement:
"It is false that the band plays rock music or the band has a guitarist."

This can be represented logically as:
\[
\neg (\text{R} \vee \text{G})
\]
Where:
- \( R \) = "The band plays rock music"
- \( G \) = "The band has a guitarist"
- \( \neg \) = "It is false that"
- \( \vee \) = "or" (logical disjunction)

### Applying De Morgan's Law:
De Morgan's Law states that:
\[
\neg (P \vee Q) \equiv (\neg P) \land (\neg Q)
\]
So, we rewrite the statement as:
\[
\neg R \land \neg G
\]

### Interpretation:
"The band does not play rock music and the band does not have a guitarist."

Thus, the equivalent statement is:
"The band does not play rock music and the band does not have a guitarist."

Would you like further clarification on this, or do you have any questions?

Here are 5 related questions to consider:
1. What are the two De Morgan's Laws in logic?
2. How would you apply De Morgan's Laws to a conjunction statement (AND)?
3. Can you provide another example where De Morgan's Laws are useful?
4. How would you negate a statement that includes both an "and" and an "or"?
5. How does De Morgan's Laws relate to truth tables in logic?

**Tip:** De Morgan's Laws are crucial when working with logical negations, particularly in simplifying complex Boolean expressions.

Use De Morgan's Laws to write an equivalent statement for the given sentence. It is false that the band plays rock music or the band has a guitarist.

Learn how to apply De Morgan's Laws to rewrite logical statements. This example demonstrates converting a negative logical disjunction into a conjunction, using the statement: 'It is false that the band plays rock music or the band has a guitarist.' Suitable for students in Grades 9-12 studying Boolean algebra and logic.

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