#23- A summer day is "pleasant" if there are intermittent

[htngo12]

Hi!

The stem presents two conditions:
1) If intermittent winds & temp stays below 84F (all afternoon) then summer day is pleasant.
2) Either temp stays above 84 (all afternoon) or no wind then summer day w/ high humidity is oppressive.
Since the first part of this condition is the opp of the first part condition of 1) then I would switch it to not (temp below84)

Translating to:
1) IW &Tb84 ->P
Cp: not P-> not IW or not Tb84
2) not (not Tb84) then no wind -> HH(opp)
Cp: not HH(opp) then not (no wind) then not Tb84

Inference from 2) Tb84 then no wind then HH (opp) to get answer E)

Is my formal logic on the right path?

[Robert Carroll]

htngo,

This is a good start!

One thing to note is that "above 84" is not the logical opposite of "below 84", so using one abbreviation (and its negation) doesn't quite work in this case. If the temperature is exactly 84, then it's neither above nor below. This distinction matters! In this case, it might be more useful just to use separate abbreviations, negating each for its respective contrapositive. In any case, it's definitely necessary to track the difference between "below 84" and "not above 84", because they do differ.

Otherwise, your diagram of the first conditional and its contrapositive seems perfect.

The diagram of the second conditional needs some further adjustment. The sufficient condition contains an "or" statement, which means the sufficient condition will be compound, and the necessary condition will be "oppressive". The contrapositive then follows the rules for negating compound conditions - the negation of a compound containing "or" is a compound containing "and" with each element of the compound negated.

You do seem to have noticed that there is actually another condition in the second conditional - the conclusion about a day's being oppressive is conditioned not just on wind and temperature but also humidity. There are two ways to track this:

HH (wind or above 84 oppressive)

or

(HH + wind) or (HH + above 84) oppressive

With that advice, try diagramming each conditional again and taking each one's contrapositive.

Robert Carroll

[htngo12]

So I guess my confusion overlaps with my formal logic for LG with the either/or concept.

For the second condition:
2) Tab84 or not W -> opp
CP2: not opp ->(not Tab84 and W)

For the other condition in the second cond:
2a) H-> (Tab84 or not W -> OPP)
CP2a: (not opp -> not Tab84 & W) -> not H

Along with the first cond:
1) IW &Tb84 -> P
CP1: not P->not IW or not Tb84

Could I infer based on CP1 w/ 2a if not IW then OPP. and the second part of CP1 w/ 2 to get if not Tb84 then OPP ?

[Adam Tyson]

I would recommend staying away from any attempt to cross-pollinate these two conditional claims, htngo12. That's the kind of mistake the authors want you to make, so don't fall for it! For example, saying there is not intermittent wind is not the same as saying there is no wind, because the wind could be constant. Saying the temp is not below 84 is not the same as saying it is above 84, because it could be exactly 84. And then there's the humidity issue - the entire second condition comes into play if the humidity is high; if it isn't high, then regardless of wind and temp we will not have met our sufficient conditions and won't be able to prove anything about the necessary condition. It might not be oppressive, and yet there is no wind and temps above 84 all day, so long as the humidity isn't high.

Treat these two conditions independently. This is a classic LSAT structure - two or three statements that have similar, but not identical, terms, and the wrong answers often conflate those similar terms. Resist that temptation and you'll be doing much better!

Keep at it, you are on the right path and seem to have a generally good understanding of conditional reasoning. That's a great start!

[htngo12]

This formal logic stuff (identifying and analyzing) is a brain roller coaster. But I get what you are saying with trying to mix my interpretations.

Ok for the answer E) are was very still means (not IW), remained windless (not W), high humidity (sufficient condition met, so know for necessary condition is met (Tab84 or no W) ->OPP), temp fell below 84 between early and late afternoon (not Tb84) and OPP. Right?

[Francis O'Rourke]

Hi Ht

You are right that if the air was very still, then there was both "No Wind" and "No intermittent periods of wind".

However, it looks like you are mixing up the second sentence. High Humidity does not guarantee that either the temperature is above 84°F or there is no wind.

you previously wrote

For the other condition in the second cond:
2a) H-> (Tab84 or not W -> OPP)
CP2a: (not opp -> not Tab84 & W) -> not H

This is unfortunately not in the stimulus

Rather, the author is saying that If you have a high humidity Summer day and above 84°F temp you will have an oppressive day. Or you will have an oppressive day if you have a high humidity Summer Day and no wind.

So it's possible that there is high humidity and a cool, windy day. Having high humidity alone does not guarantee anything.

[htngo12]

Ok I think I got that part.

So would the CP of that condition look like this?

not OPP-> (not H or not Tab84)
&
(not H or W)

[Kristina Moen]

Ok I think I got that part.

So would the CP of that condition look like this?

not OPP-> (not H or not Tab84)
&
(not H or W)

You got it! So if it's not oppressive, both of those conditions must be met.

[nyc431]

Could you please explain why option B is incorrect? Thank you!

[Robert Carroll]

nyc,

The conditional in the stimulus talking about "oppressive" days is talking about "a summer day with high humidity". Certain of those days are oppressive, subject to the conditions in the rest of that statement. Summer days without high humidity are not even discussed by that conditional, so I can make no inference about whether they're oppressive.

Robert Carroll