1. Warm up Write the conditional, converse, inverse and contrapositive statements of the following, then determine the truth value of each: I will pick it if it’s in my nose. Conditional: Converse: Inverse Contrapositive: If it’s in my nose, then I will pick it. If I pick it, then it’s in my nose. If it’s not in my nose, then I won’t pick it. If I won’t pick it, then it’s not in my nose. T F F F

2. It’s homework grading time.

3. It’s Quiz Time You may use your notes if they are on the notebook you made on the first day.

4. Let’s add just a bit to our notes on logic Today, we’re going to create a definition… also known as a biconditional statement Happy Biconditional Statement Day!

5. A Biconditional Statement is a definition and must be true in conditional and converse form. p q Statement: Triangles are closed figures that have three straight sides. Conditional: If it is a triangle, then it is a closed figure with three straight sides. Converse: If it is a closed figure with three straight sides, then it is a triangle. What is the truth value? True Since both the conditional and converse are true, then we can write a biconditional: It is a triangle if and only if it is a closed figure with three straight sides.

6. Let’s take a closer look. We do not use IF and THEN….. We use IF AND ONLY IF….. abbreviated as iff It is a triangle iff it is a closed figure with three straight sides.

7. Let’s work through a couple of examples… Statement: Big dogs burp loudly. Conditional: If it’s a big dog, then it burps loudly. (what’s the truth value?) Converse: If it burps loudly, then it’s a big dog. (what’s the truth value?) Can we write a true biconditional? no Statement: Two lines intersect at a point. Conditional: If two lines intersect, they will meet at a point. (What is the truth value?) Converse: If two lines meet at a point, they have intersected. (What is the truth value?) Can we write a true biconditional? Two lines intersect iff they meet at a point.

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