Conditionals

Conditionals

Lessons

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:

pqp \to q

Where pp is the hypothesis, qq is the conclusion, and \to implies it is an "if, then" statement.
  • Introduction
    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 a3a \leq 3, then a>3a > 3

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

    c)
    If a=1a=1, b=2b=2, c=3c=3, then a+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

    b)
    I sleep for 9 hours and I am tired

    c)
    I sleep for 6 hours and I am tired

    d)
    I sleep for 5 hours and I am not tired

    e)
    I sleep for 8 hours and I am tired