I have a question regarding no. 8 and 9. Can you explain what happened there? Also, is it not that we use ~A^A instead of ~AvD?

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter2: Parallel Lines
Section2.2: Indirect Proof
Problem 12E: Which of the following statements would you prove by the indirect method? a If ACAB in ABC, then...
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I have a question regarding no. 8 and 9. Can you explain what happened there? Also, is it not that we use ~A^A instead of ~AvD?

Solution:
let
"CA>DJ .. premise - proof by contradichion.
2) u CAVB) Vuc
conditional proposition pq pVq.
3). AAnB) Vnc
De Morgan's lauw "CAVB)= mAAmB.
4(u AN c)A (u BVuC)
Distributive low puCqdo) = (pvqJ^ (pVoJ
5) AVnc)
6) ("BVuC)
Decomposing a conjuncti on 4).
commuta Hive low Pvq = qup.
uC VnA
CV D
from premise U
9) AVD
Resolution.
conditional proposition P-q upva
Hence; proved
Transcribed Image Text:Solution: let "CA>DJ .. premise - proof by contradichion. 2) u CAVB) Vuc conditional proposition pq pVq. 3). AAnB) Vnc De Morgan's lauw "CAVB)= mAAmB. 4(u AN c)A (u BVuC) Distributive low puCqdo) = (pvqJ^ (pVoJ 5) AVnc) 6) ("BVuC) Decomposing a conjuncti on 4). commuta Hive low Pvq = qup. uC VnA CV D from premise U 9) AVD Resolution. conditional proposition P-q upva Hence; proved
Given Argument is
(AVB) C.
CV D.
A → uB
(i)
: AD.
To Find Prove this bu contradiction method .
Transcribed Image Text:Given Argument is (AVB) C. CV D. A → uB (i) : AD. To Find Prove this bu contradiction method .
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