2.5 - 2.7 Extended Notes PDF

2.5 Extended Notes Lewis Carroll, author of Alice in Wonderland, was also a famous logician. Some of his most famous logic puzzles involved non-sense statements that have a logical conclusion based on the Law of Syllogism. Below are some of such puzzles. Find the logical conclusion based on the fol...

2.5 Extended Notes Lewis Carroll, author of Alice in Wonderland, was also a famous logician. Some of his most famous logic puzzles involved non-sense statements that have a logical conclusion based on the Law of Syllogism. Below are some of such puzzles. Find the logical conclusion based on the following statements. (Hint: keep in mind the contrapositive has the same truth-value as the conditional) 1. (a) All babies are illogical. (b) Nobody is despised who can manage a crocodile. (c) Illogical persons are despised. 2. (a) None of the unnoticed things, met with at sea, are mermaids. (b) Things entered in the log, as met with at sea, are sure to be worth remembering. (c) I have never met with anything worth remembering, when on a voyage. (d) Things met with at sea, that are noticed, are sure to be recorded in the log. 2.5 Extended Notes 3. (a) No interesting poems are unpopular among people of real taste. (b) No modern poetry is free from affectation. (c) All your poems are on the subject of soap-bubbles. (d) No affected poetry is popular among people of real taste. (e) No ancient poem is on the subject of soap-bubbles. 4. (a) All writers, who understand human nature, are clever. (b) No one is a true poet unless he can stir the hearts of men. (c) Shakespeare wrote “Hamlet”. (d) No writer, who does not understand human nature, can stir the hearts of men. (e) None but a true poet could have written “Hamlet”. 2.5 Extended Notes 5. (a) Promise breakers are untrustworthy. (b) Wine drinkers are very communicative. (c) A man who keeps his promises is honest. (d) No teetotalers are pawnbrokers. (e) One can always trust a very communicative person. 6. (a) I despise anything that cannot be used as a bridge. (b) Everything, that is worth writing an ode to, would be a welcome gift to me. (c) A rainbow will not bear the weight of a wheelbarrow. (d) Whatever can be used as a bridge will bear the weight of a wheelbarrow. (e) I would not take, as a gift, a thing that I despise.  2.6 Extended Notes Write a 2-column proof. 1. Given: 12 − 3(2𝑤 + 1) = 7𝑤 − 3(7 + 𝑤) Prove: 𝑤 = 3  2.6 Extended Notes Write a 2-column proof. 2. Given: 7(𝑎 + 1) − 3𝑎 = 5 + 4(2𝑎 − 1) 3 Prove: 𝑎 = 2  2.6 Extended Notes Write a 2-column proof. 3. Given: 3(𝑥 − 2) + 𝑥 = 2𝑥 + 12 Prove: 𝑥 = 9  2.7 Extended Notes Write a 2-column proof. 1. Given: 𝐴𝐵 ≅ 𝐶𝐷 A B C D Prove: 𝐴𝐶 ≅ 𝐵𝐷  2.7 Extended Notes Write a 2-column proof. 2. Given: 1 is supp. to 2; 3 is supp. to 2 Prove: 1 3 1 2 3  2.7 Extended Notes Write a 2-column proof. 3. Given: ⃗⃗⃗⃗⃗ 𝐸𝐶 bisects ∠𝐴𝐸𝐷; ⃗⃗⃗⃗⃗ 𝐸𝐷 bisects ∠𝐶𝐸𝐵 Prove: ∠1 ≅ ∠2 C D 3 1 2 A E B  2.7 Extended Notes Write a 2-column proof. 4. Given: 𝐴𝐵 ≅ 𝐶𝐷; M is the midpt. of 𝐴𝐵; N is the midpt. of 𝐶𝐷 Prove: 𝐴𝑀 ≅ 𝑁𝐷 A M B C N D  2.7 Extended Notes Write a 2-column proof. 5. Given: 𝐴𝐵 ≅ 𝐶𝐷; 𝐵𝐷 ≅ 𝐷𝐸 Prove: 𝐴𝐷 ≅ 𝐶𝐸 C A B D E  2.7 Extended Notes Write a 2-column proof. 6. Given: C is the midpt. of 𝐴𝐵, 𝐷𝐸 ≅ 𝐴𝐶 Prove: 𝐶𝐵 ≅ 𝐷𝐸 A C B D E  2.7 Extended Notes l Write a 2-column proof. 7. Given: Line l bisects 𝑋𝑌at pt. W; D is the midpt. of 𝐶𝐸; 𝑊𝑌 = 𝐶𝐷 X W Y Prove: 𝑋𝑊 ≅ 𝐷𝐸 C D E  2.7 Extended Notes Write a 2-column proof. 8. Given: 𝐴𝐵 ≅ 𝑋𝑊, 𝐴𝐵 ≅ 𝑊𝑌 X W Y Prove: W is the midpt. of 𝑋𝑌 A B