2.3 – Definitions & Biconditionals

1. 2.3 – Definitions & Biconditionals

2. Definitions • If the original conditional statement is true and the converse is true, then it is a definition. • All definitions can be written as a biconditional statement (which we will talk about in a second)

3. Example of a definition • If you are in 10th grade, then you are a sophomore. • If you are a sophomore, then you are in 10th grade. • This is true both ways, so it is a definition

4. Sopho more 10th grade 10th grade sophomore Euler diagram works both ways

5. Biconditionals • Biconditional • A statement that contains “if and only if” (iff) and is true both ways • A biconditional is true iff the original conditional statement and the converse are both true • p q … p if and only if q

6. ADJACENT ANGLES • Adjacent Angles: angles in a plane that have a common vertex and side but no common interior points. < AOB is adjacent to <BOC

7. We’ll need this for Practice 2.3 A glass cutter is a hand tool which aids in the cutting (strictly, the controlled breaking) of flat or sheet glass. The wheel is usually about 5mm diameter and made of hardened steel or tungsten carbide with its edge ground to a V-section.