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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