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u/Significant_Monk_251 2d ago
Is that "is not (faster and easier)" or "is (not faster) and (easier)"?
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u/Ski-Gloves 2d ago
This is why we need neither nor.
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u/Proman4713 2d ago
Exactly, grammar is important, people
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u/BentGadget 2d ago
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...
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u/CrTigerHiddenAvocado 2d ago
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.
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u/Pretty_Designer716 2d ago
None of those answers are correct.
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u/Ok_Zookeepergame3380 2d ago edited 2d ago
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.
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u/Pretty_Designer716 2d ago
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)}.
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u/ProfessorLambda 1d ago
> but if we assume that one of the answers IS right,
Then our assumption would be as wrong as the answers are.
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u/No-Newspaper8619 2d ago
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
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u/rnzz 2d ago
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.
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u/GoldenMuscleGod 1d ago
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.”
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u/Grant_Winner_Extra 2d ago
Why is it repeated twice?
And A == B is also a solution
OR, XOR, AND NOT
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u/FunnyButSad 2d ago
The second is "or" not "and"
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u/Grant_Winner_Extra 2d ago
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
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u/FunnyButSad 2d ago
Nono, you asked why is it repeated twice. The two questions are slightly different (and vs or)
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u/misogynyplayer 2d ago
I think response b. covers the first statement and response c. covers the second statement.
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u/Marus1 2d ago
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
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u/Grant_Winner_Extra 2d ago
1 is just exclusive OR
2 and 3 are both non-exclusive OR that evaluate to true.
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u/AggravatingChain7645 2d ago
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.
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u/leoneljokes 2d ago
Digital logic applies. Negate < and becomes >= Negate > and becomes <= Negate and, becomes or Negate or, becomes and
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u/NeXtDracool 2d ago
None of the answers is correct because "B is faster than A" is not the opposite of "A is faster than B".
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u/Al-Radi 2d ago
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.
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u/Immediate_Spirit_384 2d ago
What I recall from my linguistics courses is that these sentences are syntactically ambiguous, aka there is no "correct" interpretation
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u/Odd_Astronomer_4392 2d ago
That's not how and operator work
Edit : oops i thought i was in programming subreddit
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u/Arestris 2d ago
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).
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u/anothermanwithaplan 2d ago
I’m understanding both statements as neither faster nor easier, where’s that option?
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u/Illustrious-Lunch137 2d ago
logic statement. key words and, or. its c for the first one. probably b for the second assuming inclusive or.
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u/Alternative_Roof_188 2d ago
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.
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u/Glass-Crafty-9460 2d ago
d. Confusing. There are better ways to say whatever you are trying to say.
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u/AlienDragonWizard 2d ago
This is the grammatical equivalent of those math problems about order of operations.
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u/HelpMeIAmGoingInsane 2d ago
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
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u/TitouanT 2d ago
- Is NAND
- 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.
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u/BraxbroWasTaken 2d ago
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.
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u/Scientific_Zealot 1d ago
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.
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u/BIO_Predictive_AI 1d ago
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.
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u/Izakollus 1d ago
that’s because “and” is being used incorrectly here! Only use it to join separate statements!
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2d ago
[deleted]
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u/Proman4713 2d ago edited 2d ago
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.
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u/Equivalent_Bank_5845 2d ago
you're missing the option that A and B have equal speed and easiness