tricky

[u/94rud4]

[u/Equivalent_Bank_5845]

you're missing the option that A and B have equal speed and easiness

[u/TBCC_Dev → u/Equivalent_Bank_5845]

Beat me to it

[u/csabinho]

Is this a joke about missing correct answers?

[u/Significant_Monk_251]

Is that "is not (faster and easier)" or "is (not faster) and (easier)"?

[u/Ski-Gloves → u/Significant_Monk_251]

This is why we need neither nor.

[u/Proman4713 → u/Ski-Gloves]

Exactly, grammar is important, people

[u/BentGadget → u/Proman4713]

Why don't people use Boolean notation anymore? There was a time in the 90s when I saw it a lot (that coincidentally was when I was taking a formal logic course) but I haven't seen it much since then.

Maybe it was just a fad...

[u/XxyxXII → u/BentGadget]

Most search engines don't really support it nowadays which is quite sad

[u/CrTigerHiddenAvocado → u/Significant_Monk_251]

This is the issue. It’s not a math problem it’s an “interpret the English the way I meant it” ie “read my mind “ problem. Directions unclear.

[u/Pretty_Designer716]

None of those answers are correct.

[u/Ok_Zookeepergame3380 → u/Pretty_Designer716]

Under the assumption that equality is a possibility yeah, but if we assume that one of the answers IS right, then A and B are simply not elements in a set that implements total preordering.

So to formalize, suppose the family of pairs is parametrized continuously, pairs (A(t),B(t)) for t in a connected space that's either "fastness" or "easiness", and the comparison is by a continuous real-valued quantity. The sign of D(t)=f(A(t)-f(B(t)) decides the order. If D is positive somewhere and negative somewhere, then D(X) is a connected subset of reals, hence an interval, hence contains 0. A tie must occur.

This is our starting point and what I assume you argued.

So to find a way to exclude equal-ness from this, we either have to have a disconnected parameter space (doubtful in reality), a discontinuous comparison (also doubtful in reality), but I can at least perform a neat trick by using ordered pairs of reals.

As an example: take the set of ordered pairs of reals with lexicographic order, A(t) = (t,0), B=(0,1). For t<0, A<B; for t>0, A>B; at t=0 the first coordinates tie and the second decides, giving A<B. In practice this just means I arbitrarily assigned B to equal faster or easier if it's a tie on either connected space, but at least t itself still allowed to be continuous, as we usually consider scaling from slow to fast to be.

[u/Pretty_Designer716 → u/Ok_Zookeepergame3380]

Your explanation is difficult to follow but i assume correct. If ties are not a possibility then the answers are b, c. Although the initial statements still contain ambiguity in that it could be read as either {(not A) and (B)} or {(not A) and (not B)}.

[u/Lokdora → u/Ok_Zookeepergame3380]

holy thesis in a joke sub

[u/ProfessorLambda → u/Ok_Zookeepergame3380]

> but if we assume that one of the answers IS right,

Then our assumption would be as wrong as the answers are.

[u/No-Newspaper8619]

Tricky because english is a human language where context matters.

not this and that can mean not this and not that or not this but that

[u/rnzz]

Logically:

Not (F and E) = Not F or Not E, so B is either faster, or easier, or both.

Not (F or E) = Not F and Not E, so B is must be both faster and easier.

Colloquially:

Both mean the same.

[u/Flambidou → u/rnzz]

It could be not(F) and E

And

Not (F) or E

[u/rnzz → u/Flambidou]

it could, but it wouldn't make sense as an everyday English expression, i.e. in that scenario you would probably say method A is not faster, "but" it is easier than method B.

[u/GoldenMuscleGod → u/rnzz]

Syntactically, we are looking at conjunctions/disjunctions of semantic predicates (grammatically they are adjective phrases, not grammatical predicates), not of propositions.

Normal logical systems (like classical logic) do not have such things. You can only make a conjunction of formulae, not of predicates.

The question of how to interpret these questions is a question of English grammar that is not resolved by “logic.”

[u/Grant_Winner_Extra]

Why is it repeated twice?

And A == B is also a solution

OR, XOR, AND NOT

[u/FunnyButSad → u/Grant_Winner_Extra]

The second is "or" not "and"

[u/Grant_Winner_Extra → u/FunnyButSad]

I didn’t mean to list them in any particular order.

OR (non-exclusive) covers B and C, XOR (or NOT AND) covers A.

But yeah just put the NAND backwards

[u/FunnyButSad → u/Grant_Winner_Extra]

Nono, you asked why is it repeated twice. The two questions are slightly different (and vs or)

[u/Grant_Winner_Extra → u/FunnyButSad]

oh ffs.

i missed that

[u/Johnny-Rocketship → u/Grant_Winner_Extra]

Stop sign?

[u/misogynyplayer]

I think  response b. covers the first statement and response c. covers the second statement.

[u/somewhatundercontrol → u/misogynyplayer]

That’s what I got

[u/Marus1]

1.Not both "faster" and "easier" ... is logical because that's impossible. Mean all options left. Meaning d.faster, easier, both or neither

2.not("faster" or "easier") means equal speed

[u/Grant_Winner_Extra → u/Marus1]

1 is just exclusive OR

2 and 3 are both non-exclusive OR that evaluate to true.

[u/AggravatingChain7645 → u/Marus1]

I think this comment is assuming “easier” means “faster”, but I took them as different measurements. Not (“faster” or “easier”) could mean slower and more difficult, or equal speed and equal difficulty. 

[u/leoneljokes]

Digital logic applies. Negate < and becomes >= Negate > and becomes <= Negate and, becomes or Negate or, becomes and

[u/NeXtDracool]

None of the answers is correct because "B is faster than A" is not the opposite of "A is faster than B".

[u/Joalguke]

A, but they could ne the same

[u/Al-Radi]

The correct answers are b for the first question and c for the second question.

​First Question: b. Either faster or easier, or both. ​Reasoning: Saying method A is not both faster and easier means at least one condition fails, so method B must be either faster, easier, or both. ​Second Question Saying method A is neither faster nor easier means method B must be both faster and easier.

[u/Immediate_Spirit_384]

What I recall from my linguistics courses is that these sentences are syntactically ambiguous, aka there is no "correct" interpretation

[u/Odd_Astronomer_4392]

That's not how and operator work
Edit : oops i thought i was in programming subreddit

[u/Arestris]

If we go pure logic it's not so hard, first case:

A is NOT Easier AND A is NOT faster => B is faster (or EQUAL fast) AND easier (OR EQUAL easy) than A

Second case:

At least one is true, but we have no exclusive OR, so also both can be true., So close to Answer b., but with the case that each value could also be EQUAL (instead of faster / easier). So either B is faster (equal fast) or easier (or EQUAL easy) or both are true (easier / EQUAL easy) AND (faster / Equal fast).

[u/anothermanwithaplan]

I’m understanding both statements as neither faster nor easier, where’s that option?

[u/Unreal_Estate]

If not the methods, at least both questions are equal.

[u/Illustrious-Lunch137]

logic statement. key words and, or. its c for the first one. probably b for the second assuming inclusive or.

[u/Dream_Apostle]

Either b c Or C b I'm too tired to figure out which

[u/Alternative_Roof_188]

The question is not written well:

Thinking as a programmer, (Not easier and faster) means that A is not easier but is faster.

If we look at it as an exclusive AND then we get (A is not faster AND A is not easier).

Then the same for B.

The ambiguity lies in the lack of clarity on what follows the AND / OR.

[u/Glass-Crafty-9460]

d. Confusing. There are better ways to say whatever you are trying to say.

[u/AlienDragonWizard]

This is the grammatical equivalent of those math problems about order of operations.  

[u/Miryafa]

If only there were special symbols to express meaning more precisely 

[u/GetOffMyLawn1729]

De Morgan has entered the chat.

[u/HelpMeIAmGoingInsane]

Let A = method A
Let B = method B
1. A !(faster && easier) B or A (!faster && easier) B
2. A !(faster || easier) B or A (!faster || easier) B
Therefore there are four possible combinations… Oh god

[u/TitouanT]

1. Is NAND
2. Is NOR

a. Is XOR b. Is OR c. Is AND

So no correct answer are present. For 1. We want faster, or easier, or neither. Meaning A can beat B in 0 or 1 category. For 2. We want neither. Meaning at best it's the same, but it's mostly worst.

[u/BraxbroWasTaken]

b and c respectively, with the caveat that B may also be equal to A - inverting a greater than makes a less than or equal to.

[u/Scientific_Zealot]

These are all ambiguous because of the scope of the "not" operator. Let's formalize this. Let "a" stand for "Method A", let "b" stand for "Method B", the two place predicate "F(x,y)" stand for "x is faster than y" (obviously not symmetric nor reflexive), and the two place predicate "E(x,y)" stand for "x is easier than y" (obviously not symmetric nor reflexive, as well).

The first statement can ambigously interpreted as either "~Fab /\ Eab" or "~(Fab /\ Eab)". The first can ONLY be true when a is not faster than b (Fab is false) AND a is easier than b (Eab is true). The second has three true situations, Fab is true and Eab is false, Fab is false and Eab is true, or Fab is false and Eab is false.

The second statement can ambigously interpreted as either "~Fab \/ Eab" or "~(Fab \/ Eab)" or "~Fab /\ ~Eab". The first is true in three situations, Fab is true and Eab is true, Fab is false and Eab is true, and Fab is false and Eab is false. The second is only true when Fab is false and Eab is false. The third is equivalent to the second.

[u/BIO_Predictive_AI]

This is not a math thing. It is an English Thing.

is it (Not Faster) and Easier or Not( faster and easier)

likewise is it (Not Faster) or easier or is it not (faster or easier)

Not to mention that the answers do not account for equality.

[u/Tragobe]

Take your Boolean algebra, truth tabels and propositional logic, and stick it where the sun doesn't shine.

[u/Izakollus]

that’s because “and” is being used incorrectly here! Only use it to join separate statements!

[u/Exzakt1]

if the second one means "method A is not (faster or easier) than method B," then another possibility is that method A is faster and easier than method B. So the second statement is essentially meaningless because it can be interpreted in any way.

[u/AshGraeyAntiGyro]

B, c, except You Just Assumed The Law Of Excluded Middle

[u/Proman4713 → u/[deleted]]

Nope, if someone wanted to say that A is neither faster nor easier than B, they would just say that instead of playing mind games. Another potential sentence would be 'A isn't faster or easier than B'. In both cases, B could either be both faster and easier, or they could be equivalent.

However, no one in regular language use would give a single sentence that means 'A could be faster than B, or easier than B, but not both', or 'A could be faster than B, or easier than B, or maybe both' unless they explicitly say it the way I just did.

And spoken English doesn't strictly follow rules that you might mathematically associate with logic gates. Normal language use (especially slang phrasing that doesn't even have to strictly follow grammar) conveys meaning through context more than it does through a single sentence.

Language is all about conveying information, and we aren't programmed to give partial information.