Math Problem Statement

If you don't study for a test, then you won't get a passing score. Write the counseling office's statement in symbolic form using p and q.

Solution

For part (a), we are asked to write the counseling office's statement in symbolic form using pp and qq.

  • pp: "You study for a test."
  • qq: "You get a passing score."

The statement given is: "If you don’t study for a test, then you won’t get a passing score." In logical terms, this is a conditional statement with negations involved.

The correct symbolic form for this would be:
pq\sim p \rightarrow \sim q
This means "If not pp, then not qq," which translates to "If you don’t study for a test, then you won’t get a passing score."


Now for part (b), based on the table provided, we are supposed to fill out the truth values.

  • The first row represents pp (studied for a test) and qq (passed the test).
  • We need to add a column for p\sim p and q\sim q and evaluate the truth values for the expression pq\sim p \rightarrow \sim q.

To proceed with this, can you provide the specific truth values for pp and qq (True or False) for this scenario?


Let me know if you want further clarification, and here are some questions you might find helpful to expand your understanding:

  1. What is the difference between a conditional and a biconditional statement?
  2. How do truth tables help evaluate logical statements?
  3. What are the logical negations of both pp and qq?
  4. How does a conditional statement differ from a conjunction?
  5. What happens to the truth value when both pp and qq are false?

Tip: Understanding how truth tables work for different logical connectives will help you analyze complex statements easily!

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Math Problem Analysis

Mathematical Concepts

Logic
Conditional Statements
Negation
Truth Tables

Formulas

Conditional statement: p → q
Negation: ¬p
Conditional negation: ¬p → ¬q

Theorems

Truth table for conditional logic

Suitable Grade Level

Grades 9-12