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- Decide which points are counterexamples to a claim about distance from the origin.P(2, 2)P(5, -1)P(3, 3)P(4, 0)
- Give a counterexample to each false claim and show it meets every hypothesis.
- Test whether points with given distances are a counterexample, then find one off a line.
- Give a counterexample to each false claim about angles, segments and lines.
- Use edges of a box to disprove a claim about perpendicular lines.
- Find the step in Owen's proof that needs extra information about x, and use it to build a counterexample.
- Find a truth table row that is a counterexample to a claim about negation.
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Counterexample: the lesson ›More Chapter 1 worksheets: Points, lines, planes and the language of proof
- 1.1Axioms, definitions and theorems
- 1.2Points, lines and planes
- 1.3Lines and planes in space
- 1.4The midpoint formula
- 1.5Conjecture, and why a pattern is not a proof
- 1.6Counterexample
- 1.7Inductive reasoning
- 1.8Deductive reasoning
- 1.9Statements and negation
- 1.10Conditionals, converse, inverse, contrapositive
- 1.11Biconditional
- 1.12Converses and biconditional definitions