Skip to content

Conditional Statement Truth Explorer

Run Fullscreen

About This MicroSim

This interactive tool helps students understand when conditional statements (if-then statements) are true or false. By toggling the truth values of the hypothesis and conclusion using on-canvas buttons, students can observe how the overall statement's truth value changes in real time.

How to Use

  1. Click the green/red Hypothesis toggle button to switch the hypothesis between TRUE and FALSE
  2. Click the green/red Conclusion toggle button to switch the conclusion between TRUE and FALSE
  3. Observe the result banner, arrow color, and truth table highlighting update immediately
  4. Click Random Example to cycle through 10 different geometric conditional statements
  5. Notice that the only FALSE case is when a TRUE hypothesis leads to a FALSE conclusion

Key Insight

A conditional statement is only FALSE when the hypothesis is TRUE but the conclusion is FALSE. This is the essence of a counterexample -- a case where the "if" part is satisfied but the "then" part fails.

Truth Table

Hypothesis (p) Conclusion (q) p -> q
T T T
T F F
F T T
F F T

Iframe Embed Code

<iframe src="https://dmccreary.github.io/geometry-course/sims/conditional-truth-explorer/main.html"
        height="502px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Learning Objectives

  • Apply truth value rules to evaluate conditional statements
  • Identify counterexamples (when a true hypothesis leads to a false conclusion)
  • Understand why conditional statements can be true even when parts are false

Bloom's Taxonomy Level

Applying -- Students apply truth value rules to evaluate conditional statements by testing different input combinations.

Target Audience

High school geometry students (grades 9-12) studying logic and proof (Chapter 2).

Prerequisites

  • Understanding of conditional statement structure (hypothesis and conclusion)
  • Familiarity with "if-then" language in geometry

Activities

  1. Predict and Test: Before clicking a toggle, have students predict whether the statement will be TRUE or FALSE, then verify
  2. Find the False Case: Challenge students to find the one combination that makes the conditional FALSE
  3. Real-World Analysis: For each random example, discuss whether the statement is actually true in geometry and what a counterexample would look like
  4. Truth Table Construction: Have students build the truth table on paper first, then verify with the MicroSim

Assessment

  • Can students correctly predict the truth value before toggling?
  • Can students explain why F -> T is considered TRUE?
  • Can students identify a counterexample for a false geometric conditional?

Duration

10-15 minutes

References

  1. Truth Tables - Khan Academy - Overview of truth tables and logical connectives
  2. Conditional Statements in Geometry - Introduction to if-then statements in geometry