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Playlist Logic and Proof 15 videos
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Indirect proofs (or proofs by contradiction) prove their conclusion by showing that the opposite cannot be true. You can use this in math and in ar...
Logical Reasoning (Problem) 290 Views
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Description:
Sounds logical to us!
Transcript
- 00:07
Adam, Bob, and Charles want to lose weight so they can look their most fabulous for the [Adam, Bob and Charles dressed in bright purple and pink clothing]
- 00:11
Mardi Gras drag parade.
- 00:13
When they first got fitted for their purple-and-green feathered jumpsuits, Adam was heavier than [Adam, Bob and Charles being fitted for their costumes]
- 00:17
Bob, who was heavier than Charles.
- 00:19
If Adam loses forty pounds, Bob loses fifteen pounds, and Charles loses twenty-five pounds
Full Transcript
- 00:24
by Mardi Gras…
- 00:26
… which of the following cannot be true of their weights on the big day?
- 00:30
And here are the potential answers…
- 00:33
Based on the wording of the question, any answer that might be true… is an incorrect
- 00:37
answer.
- 00:38
Starting from the bottom...
- 00:40
For this example, we'll say that Adam weighed three-hundred pounds, Bob weighed one-hundred-ninety-nine [Adam, Bob and Charles in a line with their weights by their side]
- 00:45
pounds and Charles weighed one-hundred-fifty pounds...
- 00:48
After Adam loses forty pounds and Charles only loses twenty-five pounds, Charles will
- 00:52
still weigh less than Adam...
- 00:54
This situation could be true, so “E” is wrong.
- 00:57
By the same logic, if Bob lost 15 pounds and Adam lost forty, Bob would still weigh less than Adam [Adam and Bob stood together with boards of their weight loss]
- 01:03
So D is also wrong
- 01:05
Now, consider a case where Adam only weighs one pound more than Bob at the start.[Adam and Bob on either side of a weighing scale]
- 01:09
This satisfied the initial condition that Adam is heavier than Bob.
- 01:12
However, after Adam loses forty pounds...
- 01:15
…by taking off that giant beehive wig...
- 01:18
…and Bob only loses fifteen pounds, Adam will weigh less than Bob. [Adam weighing less than Bob on the weighing scale]
- 01:22
“C” is possible, and therefore…it’s not the choice we’re looking for.
- 01:26
Similar to option “C”, consider a case where Adam is one pound heavier than Bob,
- 01:30
who is one pound heavier than Charles.
- 01:33
After Adam loses an insane forty pounds...
- 01:35
Adam will now weigh less than both Bob and Charles.
- 01:37
“B” is possible, and wrong [Answer B ruled out with a red cross]
- 01:40
Finally, “A” must be the correct answer by process of elimination.
- 01:43
Just to check… can this statement be proven false as well?
- 01:48
Because Charles is losing more weight than Bob, and because he's already lighter, he
- 01:52
can never end up heavier... so there you go.
- 01:56
Now that this problem's solved, we're off to get more beads. [Adam Bob and Charles waving in their drag costumes]
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