chapter 2

inverse

If not p, then not q.

disproving conjectures

to show that a conjecture is true you must show and in order to prove false you need evidence

truth tables

truth truth false false true false true false

CONTRAPOSITIVE if you are not a musician then you are not a guitar player

true

^

and conjunction

conditional statement If it is raining then there are clouds in the sky.

hypothesis and conclusion "If then" (CAPITAL IS HYPOTHESIS and lower case is conclusion) IF IT IS RAINING then there are clouds in the sky

laws of detachment

if a hypothesis of a true conditional statement is true the the conclusion is also true IF P -D(ARROW) Q IS TRUE THEN...

biconditional

if and only if

contropositive

if not q then not p

CONDITIONAL

if p then q

CONVERSE

if q then p

perpendicular lines

if two lines intersect to form right angle

law of syllogism

is hypothesis p the conclusion q if hypothesis a then r

V

OR DISCONDITIONAL

TRUTH TABLE

ALWAYS USE P-IT IS RAINING Q- I WILL TAKE YOU SURFING

IF THEN FORM if you are a guitar player, then you are a musician.

TRUE

LAW OF DETACHMENT

...

LAWS OF LOGIC

...

biconditional statement

A statement that contains the phrase "if and only if"

USEFUL FACT 2

COMPLEMENTARY ANGLES- 90( REASON- IF SOMEONE IS 90 THEN YOU COMPLEMENT THEM ON MAKING IT SO FAR AND HOW THEY LOOK) : D

GIVEN- IF A PET IS A RABBIT, THEN IT EATS CARROTS,JENNIES PET EATS CARROTS CONCLUSION- JENNIES PET IS A RABBIT TRUE OR FALSE

FALSE

INVERSE if you don't play a guitar you are not a musician

FALSE even if you don't play a guitar you can be a musician

CONVERSE if you are a musician then you are a guitar player

FALSE not all musicians play guitar

USEFUL FACT

SUPPLEMENT ANGLES- 180 (REASON- IF SOMEONE IS 180 THEN YOU SUPPLY THEM WITH LOTS OF MEDICINE) ;D

symbolic notation

let p be the angle that is a right angle and q be 90

negation

opposite of the original statement