Answered: Given: 23 = Z1 Prove: АВ АС 2 3/6 E

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Prove: LCBA = LDBA Key steps of proof: a. OC = OD M b. ДCАО — ДDAO с. LCAО LDAO d. ДCAB ДDAB e. LСВА E LDBA B
100 1. Given that P(A) = 1/5, P(B) = 1/3, P(C) = 2/5, P(A/B) = 1/2 and P(BOC) = 0 a. Find P(BIA) со PC AUB= PCVSU 1/3) Αυτ РС уз 2 PCV/5)+ P(13) 2 5 b. Find P(AUB) PCAUB) = PCA) + PCB) PCV5) +C13) 13 c. Find P(ANBNC) .5 mutlu PC^= P(1/6] + PC 1/3) + P(2/5) - (PYSA113) = 2 M/J S
Prove that
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! G: 34 7 11 О А О в о C о D (.673)- 0 = B. None of them с.п D. 18 20
3. Use C.P. or I.P. or both to construct proofs for the following (= Unit 9 -plus the rules from Units 7 and 8) [0.75 mark each]. a. A (BVC), C = (E. F), ~ (F v B) /.. ~ A b. A (XY), B = (Dv~F), ~(Dv W), F = ~Y. (A. B) > ~ X c. A 7. T (E (BVC)), S = ~(Dv C), T (S. ~ B), ~ Av C (DVE) 1 [Extra credit, 1 mark] d. (C. (F v E)) v (C. ~ (F v E)), F~B, (AC) = ~ (X > E) /.. B > C
1 Q4: Evaluate 22 dz, C: \z-3i+5 = 9. Sc z²+25
3. Use C.P. or I.P. or both to construct proofs for the following (= Unit 9 -plus the rules from Units 7 and 8) [0.75 mark each]. a. A (BVC), C = (E. F), ~ (F v B) /.. ~ A b. A (XY), B = (Dv~F), ~(Dv W), F = ~Y. (A. B) > ~ X c. A 7. T (E (BVC)), S = ~(Dv C), T (S. ~ B), ~ Av C (DVE) 1 [Extra credit, 1 mark] d. (C. (F v E)) v (C. ~ (F v E)), F~B, (AC) = ~ (X > E) /.. B > C
Use the Levi-Civita symbol eijk and Kroneker delta dij to show that
Students are asked to prove the following statement: Theorem: A - (BNC) = (A − B)~ (A − C). One student provides the following proof: Disproof: Note that A (BNC) = An (BC) = An (BCUCC) = (ANB) U (ANC) = (A - B) U (AC) (A - B) n(A - C) ● by set difference law by DeMorgan's law by distributive law by set difference law Is the student's proof correct? If the student is correct, then fill in the needed to • make the proof completely correct • make sure each assertion made is fully justified • make the proof written in such a way that a student in the class could follow the logic and be fully convinced that the theorem is true. If the student is incorrect, then • Identify any errors in the proof above. Explain each error. Your explanation should be written to the student who made the error, and should try to help the student understand why what they wrote is incorrect.
The graph ofg (x) x2 is given. 7. V The function u (x) was obtained g (x) and is graphed below. What is u (x)? и (х) 3 (х + 5)2 а.
2. Which of the following țtvas is a model for the following formula? P+ (-(Q ^ R) V s) Р: T Q: T (A) R: T S: F Р: F Q: F R: F (В) S: T Р: F Q: T R: T (C) S: F

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