Inverses, converses, and contrapositives  Logic
Inverses, converses, and contrapositives
Lessons
Notes:
Let $p$ be the hypothesis and $q$ be the conclusion. Then:
An inverse statement is formed by negating both the hypothesis and conclusion of the conditional. In symbolic form it would be:
~$p$ $\to$ ~$q$
A converse statement is formed by switching the hypothesis and the conclusion of the conditional. In symbolic form it would be:
$q\ \to p$
A contrapositive statement is formed by negating both the hypothesis and conclusion, AND switching them. In symbolic form it would be:
~$q$ $\to$ ~$p$
Statements which always have the same truth values are logical equivalents.
Conditionals and contrapositives are logical equivalents, and inverses and converses are logical equivalents.

Intro Lesson
The inverse, converse, and contrapositive Overview:

1.
Finding the inverse, converse and contrapositive
Given the statements, write the inverse, converse, and contrapositive: 
2.
For each statement, write the inverse, converse, and contrapositive in symbolic form:

3.
Truth value of inverse, converse and contrapositive
Write the converse, and find the truth value of the converse: 
4.
Assume that the conditional statement is true. Write the inverse and state whether the inverse is always true, sometimes true, or never true:

5.
Logical Equivalents
Find the truth value of the following conditionals. Then write the contrapositive and find the truth value of the contrapositive. Are the truth values the same?

6.
Finding truth values of original statements
Find possible truth values for $p$ and $q$ where: