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Day 1: Conditional Statements
How can logic be used to justify geometric reasoning?
Conditional Statement, Hypothesis, Conclusion, Truth Value, Counterexample
A logical statement with two parts, written in "if-then" form.
If you get a 100 on the test, then you get a sticker.
If hypothesis, then conclusion.
The part of the statement that follows the "if". It's the condition.
The part of the statement that follows the "then". It's the result.
If it is raining, then the ground is wet.
Hypothesis (p): "it is raining"
Conclusion (q): "the ground is wet"
We can write conditional statements using symbols to save time.
"If p, then q" is written as:
p → q
(The arrow means "implies")
This is called the Truth Value of the statement.
A counterexample is an example where the hypothesis is true, but the conclusion is false.
If a shape has four sides, then it is a square.
Is this statement TRUE or FALSE?
FALSE
What is a counterexample?
(A rectangle, a rhombus, a trapezoid...)
Choose your level and solve the problems.
1. Statement: "If an angle measures 90°, then it is a right angle."
Identify the hypothesis and conclusion.
2. Statement: "If x = 5, then 2x = 10."
Identify the hypothesis and conclusion.
1. Rewrite in "if-then" form: "All squares are rectangles."
2. True or False? If false, give a counterexample: "If a shape has four equal sides, then it is a square."
1. Create your own true conditional statement about a geometric figure.
2. Create your own false conditional statement about numbers. Provide a counterexample.
On your notecard, analyze the statement:
"If a student plays basketball, then they are tall."
1. Identify the hypothesis and conclusion.
2. Is this statement true or false? Why?