Logical Reasoning

PT105 · S4 · Q17 Everyone who is excessively generous

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Everyone who is excessively generous is not levelheaded, and no one who is levelheaded is bold.

Statements

conditional (everyone = sufficient condition)

Excessively generous → Not levelheaded Levelheaded → Not excessively generous

conditional (no A's are B = all A's are ~B)

Levelheaded → Not bold Bold → Not levelheaded

Evaluate

Whenever we're doing Inference questions and are given any conditional ideas, we think two things: 1. can I chain this conditional up with any others? 2. can I apply this conditional (often via contrapositive) to any facts provided?

In this case, both claims are conditional, so #2 is out.

But #1 is alive and well! The two statements have an overlapping term (whether or not you're levelheaded), which usually means we can chain them.

However, here we can't actually chain them. They're just trying to bait us into doing so. We were essentially given this: A → B C → B

Those don't form any A → B → C chain. All we could do would be to say something like, ~B → ~A and ~C

Goal

Look for trap answers trying to connect generosity to boldness, which we can't do, since the conditionals did not chain together.

The correct answer might play off the fact that we have "Levelheaded" show up as a trigger twice, so we could say

Levelheaded → ~Extra Generous and ~Bold

17.

Which one of the following is strictly implied by the above?

  1. Everyone who is excessively generous

    No Connection

    This is the style of trap answer we knew was coming, acting as though the concepts of generosity and boldness can be connected to each other conditionally. This answer is saying: Excessively generous ? Not bold We were told: Excessively generous ? Not levelheaded Can we get from "not levelheaded" to "not bold"? No, we were given this Levelheaded ? Not bold Bold ? Not levelheaded The only thing we know about excessively generous people is that they're not levelheaded. We don't know anything about what proportion of people who are "not levelheaded" are bold or not bold.

    15% picked this

  2. Everyone who is not bold

    Unknown Trigger

    This is another trap trying to conditionally connect the concepts of generosity and boldness, which were not connectable. This answer is saying: Not bold ? Excessively generous We were told: Levelheaded ? Not bold Bold ? Not levelheaded "Not Bold" never shows up as a trigger, so we know this answer is not something we can derive.

    3% picked this

  3. No one who is not

    Unknown Trigger

    This is another trap trying to conditionally connect the concepts of generosity and boldness, which were not connectable. The form "no one who is A is B" becomes "everyone who is A is not B" But here there will be a double negative that could mess us up. "No one who is A lacks B" becomes "everyone who is A is not lacking B", which means "everyone who is A possesses B". If I say "No one who is rich lacks a luxury car" I'm saying "everyone who is rich possesses a luxury car". So saying, "No one who is not-bold lacks generosity" is saying, "everyone who is not-bold possesses generosity". So this answer is saying the same conditional that (B) was saying, which of course would guarantee they're both wrong (because they can't both be right) Not bold ? Excessively generous

    7% picked this

  4. Correct

    If someone is levelheaded, then

    Why this is right

    We had these conditionals: Excessively generous ? Not levelheaded Levelheaded ? Not excessively generous Levelheaded ? Not bold Bold ? Not levelheaded As we can see from the 2nd and 3rd line, if someone is levelheaded than they are not excessively generous and not bold. When we say, "If A, then neither B nor C" it looks like, "A ? ~B and ~C" So this answer is saying Levelheaded ? ~Bold and ~Excessively Generous

    Skill tested: Must be True · how this choice captures the argument's function is the move to repeat next time.

    69% picked this

  5. If someone is not levelheaded,

    Unknown Trigger

    These were the conditionals we were given. Excessively generous ? Not levelheaded Levelheaded ? Not excessively generous Levelheaded ? Not bold Bold ? Not levelheaded This answer choice starts with the trigger "If not levelheaded". We don't have that trigger, so this answer is doomed.

    6% picked this

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