If a quadrilateral is a square, then it has 4 right angles.

What is p?

A quad is a square

What is the conclusion?It has 4 right anglesWhat is the converse?If a quadrilateral has 4 right angles, then it is a square.

What is the inverse?

If a quad is not a square, then it does not have 4 right angles

What is the contrapositive?If a quad does not have 4 right angles, then it is not a square.Is the inverse true or false?

False, it could be a rectangle.

If a quadrilateral is a square, then it has 4 right angles.

m w~r ~wp mWhat conclusion can you draw?

p r (p m w r) OR

~r ~p (~r ~w ~m ~p)

Construct a truth table for (pΛ~q)ᴠr .

p q ~q (pΛ~q) r (pΛ~q)Vr

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

FFTTFFTT

FFTTFFFF

TFTTTFTF

Given: Diagram as shown. Prove: angle 1 congruent angle 2

1 2

Statements Reasons

1. <1 & <2 are right <s 1. Given (assumed from diagram is ok)

2. <1 = <2 2. Right angle Thm (if 2 angles are right <s, then they are congruent)

Statements Reasons

1. <1 & <2 are right <s 1. Given (assumed from diagram is ok)

2. <1 & <2 are both 90˚

2. Def right angle

3. <1 = <2 3. Def congruent angles

If an animal is a zebra, then it is mammal.

What is the inverse?

If an animal is NOT a zebra, then it is not a mammal.

What is the contrapositive?If an animal is not a mammal, then it is not a zebra.Is the inverse true or false?False, the mammal could be a human.

What is p?

An animal is a zebra

What is q?It is a mammalWhat is the converse?If an animal is a mammal, then it is a zebra.

If an animal is a zebra, then it is mammal.

Construct a truth table for (~p ᴠ q)ᴠ~r

p ~p q (~pVq) r ~r (~pVq)V~r

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

FFFFTTTT

TTFFTTTT

FTFTFTFT

TTFTTTTT

Given: Diagram as shown. Prove: angle BAT congruent angle CAR

C

AR

B

T

Statements Reasons

1. <CAR & <BAT are straight <s

1. Assumed from diagram

2. <CAR = <BAT 2. if 2 angles are straight <s, then they are congruent

Statements Reasons

1. <CAR & <BAT are straight <s

1. Assumed from diagram

2. <CAR & <BAT are both 180˚

2. Def straight angle

3. <CAR = <BAT 3. Def congruent angles

r w~t ~sa rt aWhat conclusion can you draw?

s w (s t a r w) OR

~w ~s (~w ~r ~a ~t ~s)

If an angle measures 100˚, then it is NOT acute.

What is the inverse?

If an angle is not 100˚, then it is acute.

What is the contrapositive?If an angle is acute, then it doesn’t measure 100˚.Is the inverse true or false?False. Counterexample?150˚ (a 150˚angle is not 100˚, but is also not acute.)

What is the hypothesis?

An angle measures 100˚

What is the conclusion?It is not acuteWhat is the converse?If an angle is not acute, then it measures 100˚

If an angle measures 100˚, then it is NOT acute.

Construct a truth table for (pV~q)Λr

p q ~q (pV~q) r (pV~q)Λr

T T T

T T F

T F T

T F F

F T T

F T F

F F T

F F F

FFTTFFTT

TTTTFFTT

TFTFFFTF