## Related Conditional: converse, inverse, contra- positive-

#### Aligned To Common Core Standard:

**High School Geometry** - HSG-MG.A.3

What Are Related Conditionals: converse, inverse, contra-positive?
We all like to know the truth- the truth that clears our doubts and offers us a better understanding. But the question is, how do you determine whether something is true or not?
We have set two criteria of this, one that something is factual and the second that something seems logical. Over time, mathematicians and the think tanks came up with a rule to determine the statement as true or not. One such rule is known as logical equivalence. It defines the mutually supported logic of the statements. To find out a logical equivalence, we develop hypotheses and conclusions.
**THE CONVERSE** - Let's consider a conditional phrase: If I were watching television, I would be at home
Now consider this: If I were at home, I would be watching television
This new statement is the converse of the original statement. You create converse by swapping the hypothesis and conclusion. It may contain the same words but not the same truth or logic.
**THE INVERSE** -
In inverse hypothesis and conclusion are negated. So if our conditional phrase states:
If I were watching television, I would be at home.
The inverse statement would be: If I were not watching television, I would not be at home.
The logical inverse doesn't hold the truth as the conditional phrase.
**THE CONTRAPOSITIVE** -
In logical contrapositive statement we negate both hypothesis and conclusion and then switch them.
If our conditional phrase is: If I were watching television, I would be at home | Contrapositive statement would be: If I were not in my home, I would not be watching television
These worskeheets help students make sense of logic statements that include converse, inverse, contra- positive- statements.

### Printable Worksheets And Lessons

- Converse Step-by-Step Lesson- I don't know why, but Converse gets me thinking about the old shoe company. Are they still around?
- Guided Lesson - We give you a statement and ask you to rewrite it using the inverse, contra positive, or converse properties.
- Guided Lesson Explanation - I like to explain the conditional first and then apply it to the sentences.
- Practice Worksheet - It really couldn't get more straight forward then this. I tried to make the sentences as clear as possible.
- Matching Worksheet - Yes, the matching sentences make it a bit simple based on the different subjects, but it does take some thinking.
- Truth Values: and, or, implies, if and only if Five Pack of Worksheets - The basic theme of this pack is similar, but it can be a bit tricky.

#### Homework Sheets

Write the inverse as numbers and even as sentences.

- Homework 1 - A converse of a statement basically swaps the hypothesis and the conclusion of the statement. Let's identify the hypothesis and conclusion of the statement.
- Homework 2 - As we know, when we flip the conditional statement around (the hypothesis becomes the conclusion and the conclusion becomes the hypothesis).
- Homework 3 - Write the contra positive of given sentence. If he goes to the office, then he will be doing work.

#### Practice Worksheets

Remember when looking at the answers, do not take the sentences literally.

- Practice 1 - As we know, when we make the conditional statement negative (in other words when we write the inverse, we add not to the hypothesis and to the conclusion).
- Practice 2 - After taking the negation of the hypothesis and the conclusion.
- Practice 3 - The contra positive of a statement is created when you negate both the hypothesis and conclusion of a statement.

#### Math Skill Quizzes

Grading quiz 2 and 3 will require some extra reading.