Conditionals - Logic

Conditionals

Lessons

Notes:

Notes:

A conditional statement is a statement written in the form "if, then".
The phrase after the word "if" is called a hypothesis.
The phrase after the word "then" is called the conclusion.
In symbolic form the conditional statement is written as:
$p \to q$
Where $p$ is the hypothesis, $q$ is the conclusion, and $\to$ implies it is an "if, then" statement.

Intro Lesson

Conditionals Overview:
1.
Hypothesis and Conclusions
Identify the Hypothesis and Conclusion:
2.
Write each statement in "if, then" form:
3.
Truth value of Conditionals
Determine the truth value of the following conditional statements. If it is false, then find a counterexample:
4.
Determine the truth value of the statement below for each set of conditions:
If I sleep for more than 8 hours, then you will be not tired

Conditionals

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Intro Lesson: b

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Lesson: 1b

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Intro

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Don't just watch, practice makes perfect.

Do better in math today

Don't just watch, practice makes perfect.

Lessons

Notes:

Intro Lesson

Conditionals Overview:

a)

What are Conditionals?

b)

Truth Table for Conditionals

1.

Hypothesis and Conclusions Identify the Hypothesis and Conclusion:

a)

If Patsy has a messy hair today, then she will not show up to work.

b)

If two lines are parallel, then they will not intersect.

c)

If a polygon has 3 sides, then it is a triangle.

d)

If the dog is barking, then someone is nearby.

2.

Write each statement in "if, then" form:

a)

The sum of the angles of a 3-sided polygon is 180&#deg;.

b)

In a clear night, we can see the moon.

c)

Getting a bachelor's degree will get you a job.

3.

Truth value of Conditionals Determine the truth value of the following conditional statements. If it is false, then find a counterexample:

a)

If a≤3a \leq 3a≤3, then a>3a > 3a>3

b)

If two lines intersect, then it must create a right angle

c)

If a=1a=1a=1, b=2b=2b=2, c=3c=3c=3, then a+b+c>5a+b+c>5a+b+c>5

d)

If a polygon has 3 sides, then it is a triangle.

4.

Determine the truth value of the statement below for each set of conditions: If I sleep for more than 8 hours, then you will be not tired

a)

I sleep for 9 hours and I am not tired

or

Hypothesis and Conclusions
Identify the Hypothesis and Conclusion:

Truth value of Conditionals
Determine the truth value of the following conditional statements. If it is false, then find a counterexample:

If $a \leq 3$ , then $a > 3$

If $a=1$ , $b=2$ , $c=3$ , then $a+b+c>5$

Determine the truth value of the statement below for each set of conditions:
If I sleep for more than 8 hours, then you will be not tired