Math Problem Statement

If a polygon has four right angles, then it is either a square or a rectangle. What is the inverse of this conditional?

Solution

The problem asks to use the conditional statement:

"If a polygon has four right angles, then it is either a square or a rectangle."

We are tasked with finding the inverse of this conditional statement. The inverse of a conditional switches the positive and negative versions of the hypothesis and the conclusion without changing their order.

Original Conditional:

  • Hypothesis: "A polygon has four right angles."
  • Conclusion: "The polygon is either a square or a rectangle."

Inverse:

  • To form the inverse, negate both the hypothesis and the conclusion.

So, the inverse would be:

"If a polygon does not have four right angles, then it is neither a square nor a rectangle."

Would you like a detailed explanation of the steps?

Here are 5 related questions for further practice:

  1. What is the converse of the given conditional statement?
  2. How do you find the contrapositive of a conditional?
  3. Can a polygon with four right angles be something other than a square or a rectangle?
  4. How would you represent the inverse of a conditional statement symbolically?
  5. What is the difference between the inverse and the contrapositive of a conditional?

Tip: When negating a statement in logic, make sure to reverse both the hypothesis and the conclusion to correctly form the inverse.

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Math Problem Analysis

Mathematical Concepts

Conditional Statements
Logic
Geometry

Formulas

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Theorems

Inverse of a Conditional Statement

Suitable Grade Level

Grades 8-10