Math Problem Statement

Write (p ∧ q) → r as an English sentence. Let p represent: 'Kesha’s singing style is similar to Uffie’s.' Let q represent: 'Kesha has messy hair.' Let r represent: 'Kesha is a rapper.'

Solution

The logical expression given is (pq)r(p \land q) \rightarrow r, which can be translated into English using the meanings of pp, qq, and rr.

Here’s what each symbol means:

  • pp: "Kesha's singing style is similar to Uffie's."
  • qq: "Kesha has messy hair."
  • rr: "Kesha is a rapper."

The expression (pq)r(p \land q) \rightarrow r means "if both pp and qq are true, then rr is true." In other words: "If Kesha's singing style is similar to Uffie's and Kesha has messy hair, then Kesha is a rapper."

Would you like any more details or further clarification?

Here are 5 related questions you might find helpful:

  1. How would you negate prp \rightarrow r in English?
  2. How would pqrp \lor q \rightarrow r be interpreted in this context?
  3. Can you rewrite r(pq)r \rightarrow (p \land q) in English?
  4. How does the conjunction pqp \land q change if we only take one of pp or qq?
  5. What is the English meaning of (pq)¬r(p \lor q) \rightarrow \neg r?

Tip: When translating logical expressions into English, make sure to respect the order of operations (like conjunction or disjunction) to maintain the correct meaning.

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Math Problem Analysis

Mathematical Concepts

Propositional Logic
Logical Expressions

Formulas

(p ∧ q) → r

Theorems

Implication in Logic

Suitable Grade Level

Grades 9-12