Logical Reasoning

PT111 · S3 · Q18 If there are any inspired performances

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If there are any inspired performances in the concert, the audience will be treated to a good show.

Statements

conditionals (if, unless, must)

If = left side

inspired → good performances show

Unless = if-not

not sophisticated → not good listeners in audience show

Must = right side

sophisticated → understand one's listener musical roots

Evaluate

Whenever we see conditional logic on a Must Be True / Most Supported question, we ask ourselves these questions:

1. are there any other conditional statements that could be chained together with this one?

2. can I apply this conditional statement to any fact that was provided (often via the contrapositive)?

In this stimulus, there were three conditionals, so there's a good chance some stuff chains together. Are there overlapping terms? Yes! Two of them mention "good show", and two of them mention "sophisticated listener". So let's see if we can chain them together (we might need to contrapose).

The 2nd sentence uses "unless". One legal way to translate any "unless" statement is to take either one of the ideas, negate it, and put that on the left of the arrow (i.e. if-not). Put the other idea, as is, on the right of the arrow. That's how we translated it up above.

Another option, when we hear "you won't have X unless you have Y" is simply to rephrase that as "X requires Y", which looks like X → Y.

So we could have said, "A good show requires sophisticated listeners" and then diagrammed it like "Good show → sophisticated listeners". This formulation makes it easier to see how these three chain together.

inspired → good → sophistic → underst performances show listeners m. roots

Goal

Look for an answer we can derive from that chain of conditional logic, or from the contrapositive chain, which says, .

18.

If all of the statements above are true, which one of the following must also be true?

  1. Correct

    If there are no sophisticated

    Why this is right

    This is the chain we have. inspired ? good ? sophistic ? underst performances show listeners m. roots This answer is derivable by contrapositive. We know, not ? not ? not ? not 4th 3rd 2nd 1st This is testing us on that not-3rd implies not-1st subset of the chain. Here's the contrapositive chain: don't not not not und ? sophis ? good ? inspired roots listeners show performances We can definitely derive this connection. Why are they testing a 3 to 1 connection rather than a 4 to 1 connection? No reason. They just like to keep us guessing. We assume they'll want to test the bookends of the chain, to reward us for putting the whole thing together, but they sometimes just test some subset of the chain.

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

    63% picked this

  2. No people who understand their

    Illegal Negation

    This answer is doing an illegal negation of the chain we have. This is what we know: inspired ? good ? sophistic ? underst performances show listeners m. roots This is what this answer is saying: not good ? don't understand show musical roots We can't take a chain that says, 1 ? 2 ? 3 ? 4 and derive not 1 ? not 2 ? not 3 ? not 4 That's an illegal negation, which is never a valid inference in conditional logic.

    9% picked this

  3. If there will be people

    Illegal Reversal

    This answer is doing an illegal reversal of the chain we have. This is what we know: inspired ? good ? sophistic ? underst performances show listeners m. roots This is what this answer is saying: understand ? inspired musical roots performance We can't take a chain that says, 1 ? 2 ? 3 ? 4 and derive 4 ? 1 That's an illegal reversal, which is never a valid inference in conditional logic.

    8% picked this

  4. The audience will be treated

    Illegal Reversal

    This answer is doing an illegal reversal of the chain we have. This is what we know: inspired ? good ? sophistic ? underst performances show listeners m. roots This is what this answer is saying: understand ? good musical roots show When we're diagramming this answer choice, which uses unless, we can apply the "if-not" to either idea in the conditional. "If audience not treated to good show, there are people who don't understand their musical roots" not good show ? not understand roots (If we diagrammed it this way, we would have called this an illegal negation of our chain) "If there are not people who do not understand their roots, then good show" (This is how we diagrammed it above. The double-negative of "there are not people who don't understand" becomes "the people do understand") We can't take a chain that says, 1 ? 2 ? 3 ? 4 and derive or derive 4 ? 2 not 2 ? not 4

    13% picked this

  5. If there are sophisticated listeners

    Illegal Reversal

    This answer is doing an illegal reversal of the chain we have. This is what we know: inspired ? good ? sophistic ? underst performances show listeners m. roots This is what this answer is saying: sophisticated ? inspired listeners performances We can't take a chain that says, 1 ? 2 ? 3 ? 4 and derive 3 ? 1 That's an illegal reversal, which is never a valid inference in conditional logic.

    7% picked this

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