Geometry 2 3 Deductive Reasoning Using Symbolic Notation

Geometry 2. 3 Deductive Reasoning

Using Symbolic Notation If the sun is out, then the weather is good. p q Conditional statement can be written symbolically as follows: If p, then q p q

Converse Switch p and q If q, then p or q p

Biconditional Statement If p, then q and if q, then p Or p q Or p if and only if q

Example Let p be “the value of x is -4” and q be “the square of x is 16. ” a) Write p q in words. b) Write q p in words. c) Decide whether the biconditional statement is true.

Inverse and Contrapositive • Inverse: ~ p ~ q • Contrapositive: ~ q ~ p

Example Let p be “today is Monday” and q be “there is school. ” a) Write the contrapositive of p q in symbols and words. b) Write the inverse p q in symbols and words.

Deductive vs Inductive • Deductive reasoning uses facts, definitions, and accepted properties in a logical order to write a logical argument. • Inductive reasoning uses previous examples and patterns to form a conjecture.

Laws of Deductive Reasoning • Law of Detachment – if p q is a true conditional statement and p is true, then q is true. • Law of Syllogism – If p q and q r are true conditional statements, then p r is true.

Examples on Worksheet Answers 7. Law of Detachment 8. Invalid 9. Law of Detachment 10. Law of Syllogism 11. Invalid 12. Law of Syllogism

Examples State whether the argument is valid. 1. Jamal knows that if he misses the practice the day before a game, then he will not be a starting player in the game. Jamal misses practice on Tuesday so he concludes that he will not be able to start in the game on Wednesday. 2. Michael knows that if he does not do his chores in the morning, he will not be allowed to play video games later the same day. Michael does not play video games on Friday afternoon. So Michael did not do his chores on Friday morning.