Geometry Lesson 2A - Conditionals PDF

GEOMETRY - LESSON 2A CONDITIONALS CONDITIONAL: another name for an if-then statement CONDITIONAL: If I am a dinosaur, then I am extinct. We can represent a conditional symbolically as: If p, then q. HYPOTHESIS CONCLUSION  formed by interchanging the hypothesis CONV...

GEOMETRY - LESSON 2A CONDITIONALS CONDITIONAL: another name for an if-then statement CONDITIONAL: If I am a dinosaur, then I am extinct. We can represent a conditional symbolically as: If p, then q. HYPOTHESIS CONCLUSION  formed by interchanging the hypothesis CONVERSE: and the conclusion of a conditional CONDITIONAL: If p, then q. A conditional and its converse say very different things. CONVERSE: Many true If q, then p. statements have false converses.  formed by interchanging the hypothesis CONVERSE: and the conclusion of a conditional CONDITIONAL: If I am a dinosaur, then I am extinct. CONVERSE: If I am extinct, then I am a dinosaur. Can we provide an example which shows that the converse is false? COUNTEREXAMPLE an example that disproves a COUNTEREXAMPLE: given statement If I am extinct, then I am a dinosaur. COUNTEREXAMPLES: (extinct but not dinosaurs) DODO TASMANIAN TIGER THE VIEW MASTER How many counterexamples are necessary to disprove a given statement? Only one!  OTHER WAYS TO WRITE A CONDITIONAL If p, then q. p implies q. p only if q. q if p. CONDITIONAL: If x + 3 = 5, then x = 2. CONVERSE: If x = 2, then x + 3 = 5. Since both statements are true, we can combine them into a single statement called a BICONDITIONAL. BICONDITIONAL: x + 3 = 5 if and only if x = 2.