Logical Reasoning

PT124 · S2 · Q2 Although Samantha likes both oolong

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Although Samantha likes both oolong and green tea, none of her friends likes both.

Statements

Sam likes O and G. None of her friends like both (they either just like O, just like G, or like neither). All of her friends like B.

Evaluate

Must Be False questions are about picking an answer that contradicts something we know. They function two common ways: 1. correct answer contradicts a conditional 2. correct answer contradicts some inference we can make by combining ideas.

Are there any conditionals?

Yes, two of them (none / all): friend of Sam → ~Like O or ~Like G friend of Sam → Like B

So a correct answer could say, . Or .. .

Are there any inferences we can make by combining ideas?

When we have to All statements about the same group, we can infer that there's Some overlap for the outcomes.

If we know All A's are B + All A's are C then we can infer some B's are C

Since we know All S's friends like B All S's friend ~like O or ~like G then we can infer there is someone who likes black tea but doesn't like both oolong and green tea.

Goal

Look for an answer that contradicts something we were told or something we can derive.

2.

If the statements above are true, each of the following could be true EXCEPT:

  1. Samantha likes black tea.

    Possible

    This doesn't contradict anything we were told. The only we know about Sam is that she likes oolong and green. Maybe she also likes black.

    4% picked this

  2. None of Samantha’s friends likes

    Possible

    This doesn't contradict anything. All we know about Sam's friends is that they all like green tea, and all of them don't like oolong, don't like green, or both. So it's certainly possible that all her friends hate green tea.

    4% picked this

  3. Samantha’s friends like exactly the

    Possible

    This doesn't contradict anything. While it's unlikely in the real world for all friends to have matching tea preferences, it's still logically possible given the constraints of these statements.

    4% picked this

  4. One of Samantha’s friends likes

    Possible

    Sure, this doesn't contradict anything. We know that all Sam's friends either don't like oolong, don't like green, or both. So it's certainly possible that one of her friends doesn't like both.

    5% picked this

  5. Correct

    One of Samantha’s friends likes

    Why this is right

    This is impossible. How could any of her friends match Sam's tea preferences exactly? After all, Sam likes both oolong and green, whereas none of her friends like both. Sam can never match her friends when it comes to oolong and green, because Sam likes both of those two teas and all her friends like at-most-one of those two teas.

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

    83% picked this

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