Geometry: Logic with Conditional Statements, Converse, Inverse, Contrapositives

Are you introducing formal logic to your class and having trouble coming up with additional examples? Are you teaching logic for the first time and struggling with how to explain things to your class? This activity is great for the students and also for the teachers. The worksheet itself is only 1 page and includes 15 conditional statements. The students will then have to come up with the converse, inverse and contrapositive of each statement and also determine their truth value. If they are false they must provide a counter-example. After feedback from TPT users, I have added an additional format at the end that gives the students the opportunity to fill in blank tables if you prefer that to the simple 1-page format. I do think the tables are helpful for the students but if you are in a pinch, the 1-page format is easier to print! :)

These are more fun that what is usually in the math textbooks because these statements do not involve math. I have found that using math statements to introduce this topic make everything much more difficult to understand. The students like these because they get to be creative in their counter-examples. Here is an example of the types of statements that are listed.

Conditional: If you are a human being then you have ears.
The students then will write:
Converse: If you have ears then you are a human.
Inverse: If you are not a human being then you do not have ears.
Contrapositive: If you do not have ears then you are not a human being.

In this case the truth values would be: True, False, False, True.

My worksheet gives all of the answers and also explains what a good counter-example would be.

**Teaching Tip: If you look at the example above some students might say "I think the first statement is false because maybe a human had their ears chopped off." It is up to you if you want to let the kids think up these extreme examples. On one hand it can be fun and interesting to include them but then they sometimes miss the simple idea we are trying to get them to learn. I have taught it both ways and personally prefer that they don't get too carried away with their counter-examples because it tends to confuse them on the tests and they over think everything.

I have plenty of other geometry resources so please contact me if you are looking for something particular. Also, check out my other listings. If you are pleased with this download I would appreciate any feedback you would be willing to leave.

Thanks and happy teaching!


Formal Logic/Geometry: Conditional Statements and their Converse, Inverse, and Contrapositves by Dana Burrows is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.