Logic Test Review (Geometry)

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Name __________________________________________________________
Page # ________
Logic Test Review
Term
Definition
Conditional
Statement
Statementthatcanbewrittenin__________________________form.Anothernamefora
Hypothesis
Partofa_________________statementthatfollowstheword_______________
Conclusion
Partofa__________________statementthatfollowstheword______________
conditionalstatementisan______________________.
Negation
Denialofastatementformedbyaddingorremovingtheword______________froma
statement
Negate
Toaddorremovetheword__________fromastatementtochangeits_____________
_______________fromtrueto________________orfromfalseto________________
Converse
Statementformedfromaconditionalstatementby______________________________the
_____________________________and_____________________________
Inverse
Statementformedfromaconditionalstatementby______________________________the
_____________________________and________________________________
Contrapositive
Biconditional
Statement
Statementformedfromaconditionalstatementby____________________________AND
______________________the___________________________and____________________________
Combiningaconditionalstatementanditsconverseusingthephrase
“________________________________”
Conjunction
Astatementmadefromcombiningtwo___________premisesusingtheword“_______”
Disjunction
Astatementmadefromcombiningtwo___________premisesusingtheword“_______”
Symbol
Meaning
Symbol
!
∨
~
!
∧
∴
Meaning
1.) Use the following conditional statement: “If elephants fly, then fish don’t swim.”
A.) p is the hypothesis. Write p:
B.) q is the conclusion. Write q:
C.) ~p means “the negation of p.” Write ~p:
D.) ~q means “the negation of q.” Write ~q:
E.) (converse) q ! p means “q implies p” or “If q, then p.” Write q ! p:
F.) (inverse) ~p ! ~q means “Not p implies not q” or “If not p, then not q.” Write ~p ! ~q:
G.) (contrapositive) ~q ! ~p means “Not q implies not p” or “If not q, then not p.” Write ~q ! ~p:
H.) p ∧ q means “p and q.” Write p ∧ q:
I.) p ∨ q means “p or q.” Write p ∨ q:
J.) ∴p means “therefore p.” Write ∴p:
K.) p ! q means “p if and only if q.” Write p ! q:
2. Rewrite each of the following statements as a conditional statement (in if-then form). Then, circle the
hypothesis, and underline the conclusion.
a. Mark Twain wrote, “If you tell the truth, you don’t have to remember anything.”
Rewrite:
b. Helen Keller wrote, “One can never consent to creep when one feels the impulse to soar.”
Rewrite:
c. Mahatma Ghandi wrote, “Freedom is not worth having if it does not include the freedom to make
mistakes.”
Rewrite:
d. Benjamin Franklin wrote, “Early to bed and early to rise makes a man healthy, wealthy, and wise.”
Rewrite:
3. Write the converse, inverse, and contrapositive for each of the following conditional statements..
a. “I will give you a million bucks if you show me a unicorn.”
Converse:
Inverse:
Contrapositive:
b. “No animals were harmed in testing this product.”
Converse:
Inverse:
Contrapositive:
4. Given the major premise below, for each minor premise, give a conclusion if possible, and tell the rule
you are using. Otherwise, write NVC.
“If it is raining, then Sarah will not go to the football game.”
a. Sarahwillnotgotothefootballgame.
b. Itisraining. c. Sarahwillgotothefootballgame. d. Itisnotraining.
___________________________________________________________
___________________________________________________________
___________________________________________________________
___________________________________________________________
5. Let p: you see lightning and q: you hear thunder. Write each of the following statements in symbolic
notation:
a. If you see lightning, then you hear thunder.
________________________________
b. If you hear thunder, then you see lightning.
________________________________
c. If you don’t see lightning, then you don’t hear thunder.
________________________________
d. If you don’t hear thunder, then you don’t see lightning.
________________________________
e. You hear thunder and you see lightning.
________________________________
f. You see lightning or you hear thunder.
________________________________
g. You hear thunder if and only if you see lightning.
________________________________
6. Draw a Venn Diagram below for each of the following statements:
a. All squares are rhombi.
b. Some rectangles are squares.
c. No trapezoids are parallelograms.
d. All dalmations are dogs; and no
dogs are cats.
e. Allzoidsaredroids.Somedroidsare
widgets.Nozoidisawidget.
f. AllCoastalteamsarepartoftheACC.All
AtlanticteamsarepartoftheACC.No
AtlanticteamisaCoastalteam.AllACC
teamsarepartoftheNCAA
7.) Premises:
M!C
H!L
~B
L!B
C!H
Prove:
~M
8.) Premises:
A!R
E!D
P
R ! ~Q
P!Q
D!A
Prove:
~E
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