Transcript Practice for Unit 2 Quiz

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 angles
What is the converse?
If a quadrilateral has 4 right angles, then it is a
square.
If a quadrilateral is a square,
then it has 4 right angles.
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.
mw
~r  ~w
p m
What 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
T
T
T
T
T
F
T
F
F
T
F
T
F
F
F
F
F
F
T
T
F
F
T
T
(pΛ~q)
F
F
T
T
F
F
F
F
r
T
F
T
F
T
F
T
F
(pΛ~q)Vr
T
F
T
T
T
F
T
F
Given: Diagram as shown.
Prove: angle 1 congruent angle 2
1
Statements
2
Reasons
Statements
Reasons
1. <1 & <2 are right <s 1. Given (assumed
from diagram is ok)
1. <1 & <2 are right <s 1. Given (assumed
from diagram is ok)
2. <1 = <2
2. <1 & <2 are both
90˚
2. Def right angle
3. <1 = <2
3. Def congruent
angles
2. Right angle Thm (if
2 angles are right <s,
then they are
congruent)
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.
If an animal is a zebra, then it is
mammal.
What is p?
An animal is a zebra
What is q?
It is a mammal
What is the converse?
If an animal is a mammal, then it is a zebra.
Construct a truth table for (~p ᴠ q)ᴠ~r
p
~p
q
T
F
F
F
F
T
T
T
T
T
T
T
T
F
F
F
F
T
F
F
T
T
F
F
(~pVq)
T
T
F
F
T
T
T
T
r
~r
T
F
T
F
T
F
T
F
T
F
T
F
T
F
T
F
(~pVq)V~r
T
T
F
T
T
T
T
T
Given: Diagram as shown.
Prove: angle BAT congruent angle CAR
B
C
A
Statements
Reasons
R
Statements
1. <CAR & <BAT are
straight <s
1. Assumed from
diagram
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
2. <CAR = <BAT
T2. if 2 angles are
straight <s, then they
are congruent
Reasons
rw
~t  ~s
a r
ta
What 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.)
If an angle measures 100˚, then
it is NOT acute.
What is the hypothesis?
An angle measures 100˚
What is the conclusion?
It is not acute
What is the converse?
If an angle is not acute, then it measures 100˚
Construct a truth table for (pV~q)Λr
p
q
~q
(pV~q)
r
T
T
T
T
F
T
F
F
T
F
T
F
F
F
F
T
T
T
T
F
F
T
T
T
T
F
F
T
T
F
F
T
T
F
T
F
T
F
T
F
(pV~q)Λr
T
F
T
F
F
F
T
F