Charlie is planning to invite four friends to a small dinner party. Unfortunately, her friends don't all get along with one another, and she doesn't expect them all to come. She knows that...1.) Brad or Cate, and perhaps even both of them, will come2.) If Brad comes then Andrew won't come3.) If Dennis doesn't come then Cate won't come either4.) If Dennis does come, then Andrew will come tooCharlie reasons that the following conclusion follows logically from premises (1)-(4)5.) Either Andrew, Cate, and Dennis all come to her dinner party and Brad does not, or else Brad is the ONLY one who comesHow does (5) follow logically from (1)-(4)?. Created by kj

Math Logic Question... So lost...?

May 2021 1 123 Report

Math Logic Question... So lost...?

Charlie is planning to invite four friends to a small dinner party. Unfortunately, her friends don't all get along with one another, and she doesn't expect them all to come. She knows that...

1.) Brad or Cate, and perhaps even both of them, will come

2.) If Brad comes then Andrew won't come

3.) If Dennis doesn't come then Cate won't come either

4.) If Dennis does come, then Andrew will come too

Charlie reasons that the following conclusion follows logically from premises (1)-(4)

5.) Either Andrew, Cate, and Dennis all come to her dinner party and Brad does not, or else Brad is the ONLY one who comes

How does (5) follow logically from (1)-(4)?

Science & Mathematics / Mathematics

Answers & Comments

holdm

Verified answer

if B comes, then by 2) Andrew doesn't. therefore, by 4(contrapositive), Dennis doesn't, if Dennis doesn't, then by 3, Cate doesn't, so if Brad comes, he comes alone.

if B does not come. then ,by 1, C comes. by 3(contrapositive) D comes, and by 4, A comes.

so, if not B, then ACD.