Reasoning and Logic

Day 1: Conditional Statements

Today's Objectives

Identify the hypothesis and conclusion of a conditional statement.
Determine the truth value of a conditional statement.
Write conditional statements in symbolic form.

Essential Question

How can logic be used to justify geometric reasoning?

Key Vocabulary

Conditional Statement, Hypothesis, Conclusion, Truth Value, Counterexample

What is a Conditional Statement?

A logical statement with two parts, written in "if-then" form.

If you get a 100 on the test, then you get a sticker.

The Two Parts

If hypothesis, then conclusion.

Hypothesis (p)

The part of the statement that follows the "if". It's the condition.

Conclusion (q)

The part of the statement that follows the "then". It's the result.

Let's Break It Down

If it is raining, then the ground is wet.

Hypothesis (p): "it is raining"

Conclusion (q): "the ground is wet"

Symbolic Notation

We can write conditional statements using symbols to save time.

"If p, then q" is written as:

p → q

(The arrow means "implies")

Is It True or False?

This is called the Truth Value of the statement.

A statement is TRUE if the conclusion always happens when the hypothesis is true.
A statement is FALSE if you can find just ONE counterexample.

A counterexample is an example where the hypothesis is true, but the conclusion is false.

Guided Practice: True or 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...)

Independent Practice

Choose the level that feels right for you and solve the problems.

RED (Developing)

Statement: "If an angle measures 90°, then it is a right angle."
What is the hypothesis? What is the conclusion?
Statement: "If x = 5, then 2x = 10."
What is the hypothesis? What is the conclusion?

YELLOW (Applying)

Rewrite in "if-then" form: "All squares are rectangles."
True or False? If false, provide a counterexample: "If a shape has four equal sides, then it is a square."

GREEN (Securing)

Create your own true conditional statement about a geometric figure.
Create your own false conditional statement about numbers. Provide a counterexample.

Exit Ticket

On your notecard, analyze the following statement:

"If a student plays basketball, then they are tall."

1. Identify the hypothesis and conclusion.

2. Is this statement true or false? Why?

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