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Four Related Conditional Statements

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About This MicroSim

This interactive diagram shows how every conditional statement has three related forms:

Form Definition Notation
Original If p, then q p → q
Converse If q, then p q → p
Inverse If not p, then not q ~p → ~q
Contrapositive If not q, then not p ~q → ~p

Key Insight

The contrapositive is ALWAYS logically equivalent to the original statement!

If one is true, the other must be true. If one is false, the other must be false.

How to Use

  • Hover over any box to highlight its logically equivalent partner
  • Click "Next Example" to cycle through different geometric statements
  • Observe how truth values relate between equivalent statements

Learning Objectives

  • Analyze the relationships between conditional forms
  • Construct converse, inverse, and contrapositive statements
  • Evaluate which forms are logically equivalent

Bloom's Taxonomy Level

Analyzing - Breaking down conditional statements into their related forms.

Iframe Embed Code

<iframe src="https://dmccreary.github.io/geometry-course/sims/four-conditionals/main.html"
        height="622px"
        width="100%"
        scrolling="no"></iframe>

References

  1. Converse, Inverse, Contrapositive - Khan Academy