4.4: Analyze Conditional Statements

If I water my flowers, then they will grow Vocabulary: a_______________________ is a logical statement that has two parts, a hypothesis and a conclusion. When it is written in an “if-then form”, the “if” part is the _______________ and the “then” part is the _____________ Example: circle the whether or not the underline phrase is the hypothesis or conclusion. If I water my flowers, then they will grow (hypothesis/conclusion) (hypothesis/conclusion) You try: If I study for my test, then I will do better on my test. __________________:when you switch the hypothesis and the conclusion __________________: when you negate (say opposite of) the hypothesis and conclusion. _________________: when you switch the hypothesis and conclusion AND negate them.

Rewrite the statement in if-then format. 1. All sharks have a boneless skeleton. 2. When n = 6, n² = 36.

If it is a shark, then it has a boneless skeleton . If n = 6, then n² = 36.

Write If-then form, converse, inverse, and contrapositive, and determine if each is true or false. Basketball players are athletes. If-then: Converse: Inverse: Contrapositive:

If-then: If they are basketball players, then they are athletes. Converse: If they are athletes, then they are basketball players. Inverse: If they are NOT basketball players, then they are NOT athletes. Contrapositive: If they are NOT athletes, then they are NOT basketball players. True or False?

Vocabulary: If 2 lines intersect to form right angles, they are _______________ lines When a statement and its converse are BOTH true, you can write them as a __________________________ statement. This statement contains “_____________”

Write a BICONDITIONAL If a polygon is equilateral, then all of its sides are congruent. Converse: Biconditional:

Converse: If all of the sides are congruent, then it is an equilateral polygon BICONDITIONAL: A polygon is equilateral if and only if all of its sides are congruent.

___________________________ 4.4: Apply Deductive Reasoning (note: different than logic in 4.2: Inductive Reasoning) Vocabulary: ____________________ reasoning uses facts, definitions, accepted properties, and logic to form logical argument. ___________________________ if the hypothesis is true, then the conclusion is true If p, then q P, therefore q ___________________________ If q, then r P, therefore r

Law of Detachment: Example: If you order desert, then you will get ice cream Sarah ordered desert Sarah got ice cream

Example: If you run every day, then you will be in good shape. Ms. Towner runs every day Ms. Towner is in good shape. 

Example: If is angle A is acute, then angle A is less than 90 degrees. Angle B is acute. Angle B is less than 90 degrees.

You Try: If an angle measures more than 90 degrees, then it is not acute. The measure of angle ABC is 120 degrees.

Angle ABC is not acute.

You Try: If two lines will never intersect, then they are parallel Lines AB and CD never intersect.

Lines AB and CD are parallel.

Law of Syllogism: Example: If you wear school colors, then you have school spirit If you have school spirit, then your team feels great. If you wear school colors, then your team feels great

Example: If you study hard, then you will do well in your classes. If you do well in your classes, then you will graduate. If you study hard, then you will graduate.

Example: If angle 2 is acute, then angle 3 is obtuse. If angle 3 is obtuse, then angle 4 is acute. If angle 2 is acute, then angle 4 is acute.

You Try: If a=bd, then c=fd If c=fd, then d=oh

If a = bd, then d = oh.

You Try: If jlt, then pql If pql, then jtw

If jlt, then jtw.

Use Inductive and deductive reasoning: Example: Make a conclusion about the sum of 2 even integers. STEP 1: Inductive Reasoning Pick a few samples: -2+4=2 ; 8+6=14 Conjecture: even# + even # = even# STEP 2: Deductive Reasoning Use logic to prove your conjecture (first write a ‘let’ statement Let n and m equal any integer

REASON b/c multiplying by 2 makes it an even number Addition factoring b/c multiplied by 2 makes an even number 3rd bullet 2n+2m=2(n+m) b/c 2n is even, 2m is even, 2(n+m) is even, and 2n+2m=2(n+m) PROOF 2n is even; 2m is even 2n+2m is the sum of even numbers 2n+2m= 2(n+m) 2(n+m) is even 2(n+m) was the sum of 2n+2m even #+even# = even #