Logical Reasoning

PT142 · S4 · Q25 Of the citizens who disapprove

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Of the citizens who disapprove of the prime minister's overall job performance, most disapprove because of the prime minister's support for increasing the income tax.

Conclusion (So)

Theresa probably approves of the prime minister's overall job performance.

Evidence

Most people who disapprove of the PM's performance do so because of the PM's support for increasing the income tax.

But, Theresa believes that the income tax should be increased.

Evaluate

Because of the symbol repetition in this argument (theresa / income tax / prime minister are all mentioned twice) and because of the quantifier most, this argument seems like a good contender for turning into an algebraic recipe.

Prem 1: Most people who are X are Y (X = disapprove of PM, Y = don't want income tax increased)

Prem 2: Person A is not Y. (A = Theresa)

Conc: Person A is probably not X.

Conversationally, we could say that . We don't know whether most people who support the tax support the PM .

There could be 100 people, 98 of whom oppose the PM. Most of those 98 oppose the PM because of the increased tax. So let's say 60 of the 98 oppose the PM because of the increased tax. That leaves 38 people who oppose the PM, but not because of the tax. And 2 people who support the PM.

If we know that Theresa is not opposed to the tax, does that mean she's more likely to be one of the 2 people who support the PM or the 38 people who oppose the PM for some reason other than the tax?

Numerically, the latter is more probable.

Goal

The conversational objection is harder to deal with, so we should probably look for our algebraic structure:

P1: Most people who are X are Y. P2: Person A is not Y. C: Person A is probably not X.

25.

Which one of the following arguments exhibits flawed reasoning that is most parallel to that in the argument above?

  1. Correct

    Of the people who support

    Why this is right

    This matches our structure really well. P1: Most people who are X are Y. Most ppl who support limited logging are thinking it'll reduce the risk of fire in the forest. P2: Person A is not Y. Andy does not link that limited logging will reduce the risk of fire. C: Person A is probably not X. Andy probably doesn't support limited logging.

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

    67% picked this

  2. Of the people who expect

    Bad Premise Match

    This is pretty close. P1: Most people who are X are Y. Most people who think the pop will increase are thinking that it's a good reason to build a new school P2: Person A is not Y. Bonita does not think population will increase. This one is botched. It's saying Person A is not X. Order is very important when it comes to Most statements.

    12% picked this

  3. Of the people who believe

    Bad Premise Match

    This is just like (B)'s problem. P1: Most people who are X are Y. Most people who think the economy is improving are thinking that because their own financial situation has improved. P2: Person A is not Y. Chung thinks the economy is not improving (in fact, it's gotten worse). This one is botched, as (B) was. It's saying Person A is not X. Order is very important when it comes to Most statements.

    8% picked this

  4. Of the people who oppose

    Bad Premise Match

    In this one, the second premise tells us that our Person is the trigger of the Most claim. P1: Most people who are X are Y. Most people who oppose funding a light rail study are thinking that the Valley Freeway should be built. P2: Person A is not Y. Donna opposes funding for a study. This is saying that Person A is X, which is not at all what we want.

    10% picked this

  5. Of the people who believe

    Bad Premise Match

    Like (D), the second premise tells us that our Person is the trigger of the Most claim. P1: Most people who are X are Y. Most people who believe there will be a blizzard are thinking that because of the weather report on Channel 9. P2: Person A is not Y. Eduardo believes there will be a blizzard tomorrow. This is saying that Person A is X, which is not at all what we want.

    4% picked this

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