Logical Reasoning

PT23 · S2 · Q10 All bridges built from 1950 to

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All bridges built from 1950 to 1960 are in serious need of rehabilitation.

Statements

On Must Be True, we're primarily scanning for Conditional or Math-y type ideas. The very first claim is conditional because of the universal "all", and the very last idea is conditional because of the universal "no".

All A's are B = A → B

All bridges built from bridge in need 1950 to 1960 are in built from → of big big need of rehab '50 - '60 rehab

No X's are Y = X → ~Y

No suspension bridges suspension not are among the bridges built bridge → faulty according to faulty design design

When we have multiple conditionals we want to see if we can chain them together. We look to see if they have any overlapping terms. We often have to contrapose one of them to see the potential link.

bridge from 50-60 → need rehab ~need rehab → ~bridge from 50-60

suspension bridge → not faulty design faulty design → ~suspension bridge

There aren't any overlapping terms, so they don't chain together. The other thing we look for when we have a conditional rule is whether there are any facts that deal with one of these triggers.

Did we get any other facts about ... 1. bridges built from 1950-1960 2. bridges that don't need serious rehab 3. suspension bridges 4. having faulty design

Yes!

Our second fact is a Some statement that deals with "faulty design".

Some bridges from have faulty design. 1950-1960

What does "faulty design" prove? faulty design → ~suspension bridge

if Some A are B, and B → C, then Some A are C.

if Some bridges from have faulty design 1950-1960

and faulty design → ~suspension bridge

then Some bridges from are ~suspension 1950-1960 bridge

Goal

Since we found a possible inference by using the contrapositive of the 2nd rule to apply to the Some fact in the 2nd sentence, we have a likely contender for an answer.

We should still stay flexible, because more than one thing can be inferred from any given paragraph, but the most likely answer is "Some bridges from '50-'60 are not suspension bridges".

10.

If the statements above are true, then, on the basis of those statements, which one of the following must also be true?

  1. Some suspension bridges are not

    Unsupported Distinction

    Is it possible that this is false? Could it be that "all suspension bridges are in serious need of rehab"? Sure. The only thing we explicitly know about suspension bridges is that none of them were built according to faulty design (through implication we also know that none of them were built from 1950 to 1960). It's possible that suspension bridges weren't built according to faulty design but are still all in serious need of some rehab. So this answer doesn't have to be true. It could be false.

    13% picked this

  2. Some suspension bridges are in

    Unprovable

    This is the flipside of our analysis of (A). Is it possible that "NO suspension bridges are in serious need of rehab"? Sure. All we know about suspension bridges is that they were all built according to good design. We have no idea what proportion of them are / aren't in need of serious rehab (something well designed will still need serious rehab at some point, depending on how old it gets). It's possible that none of them need serious rehab yet, that all of them are due for serious rehab, or any fraction in between.

    14% picked this

  3. Correct

    Some bridges that were built

    Why this is right

    Do we know of at least one bridge that is both faulty design and in serious need of rehab? Yes, simply by combining the first two claims. If we know All A's are B and Some A's are C then we know Some things are B and C If we know All bridges from 1950-1960 badly need rehab and we know Some bridges from 1950-1960 had faulty design then we know Some of these bridges are both (faulty design) and (badly need rehab)

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

    64% picked this

  4. Some bridges built from 1950

    Contradicted

    The first sentence says the exact opposite of this.

    5% picked this

  5. Some bridges that were built

    Contradicted

    If we're saying "you're not a bridge other than a suspension bridge", we're saying "you ARE a suspension bridge". So this answer is saying Some bridges with faulty design are suspension bridges. This contradicts our final claim, that all suspension bridges do not have faulty design.

    4% picked this

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