Let p and q represent the following simple statements.
​p:  I get a promotionI get a promotion.
​q:  I complete my homeworkI complete my homework.
Write the following compound statement in symbolic form.
 I do not complete my homeworkI do not complete my homework if and only if  I do not get a promotionI do not get 

The compound statement "I do not complete my homework if and only if I do not get a promotion" can be written in symbolic form using the logical symbols for negation (¬) and biconditional (↔).

Given:
- \( p \): "I get a promotion."
- \( q \): "I complete my homework."

The negations of these statements are:
- \( \neg p \): "I do not get a promotion."
- \( \neg q \): "I do not complete my homework."

The compound statement "I do not complete my homework if and only if I do not get a promotion" can be expressed as:
\[
\neg q \leftrightarrow \neg p
\]

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How would you express "I get a promotion or I do not complete my homework" in symbolic form?
2. What is the truth table for the statement \( \neg q \leftrightarrow \neg p \)?
3. How would the compound statement change if it was "I do not get a promotion if and only if I complete my homework"?
4. What does the biconditional (\(\leftrightarrow\)) symbol represent in logical statements?
5. Can the statement \( \neg q \leftrightarrow \neg p \) be simplified or rephrased logically?

**Tip:** In logical statements, the biconditional (\(\leftrightarrow\)) indicates that both sides of the statement must either both be true or both be false.

Understand the symbolic form of logical statements involving homework completion and promotion. Learn how to express complex statements using logical symbols and negations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation