i also think the “etymology” of the boolean symbols is very helpful in remembering which is which. in lattice theory, their use was inspired by similar notation in set theory. so, A ∨ B is like A ∪ B, while A ∧ B is like A ∩ B.
generally, A ∨ B is “the smallest thing that’s greater than or equal to both A and B”, while A ∧ B is “the biggest thing that’s less than or equal to both A and B”. similarly to how A ∪ B is “the smallest set that contains both A and B”, while A ∩ B is “the largest set that’s contained in both A and B”. you can also take things a step further by saying that in the context of sets, A ≤ B means A ⊆ B. doing this means that A ∨ B = A ∪ B, while A ∧ B = A ∩ B. and from this perspective, the “sharp-edged” symbols (<, ∧, ∨) are just a generalization of their “curvy” counterparts (⊂, ∩, ∪).
in the context of boolean algebra, you can set False < True, which at first may seem a bit arbitrary, but it agrees with the convention the that False = 0 and True = 1, and it also makes A ∨ B and A ∧ B have the same meanings as described above.
for some reason to remember ∩ and ∪ when I first learned it in school I visualized a mirrored symbol on top. the ∩ looked like a X which represented an intersection, while ∪ looked like an O which represented a whole. for English ∪ already looks like a U which can be thought of as short for union. that would’ve been easier.
ooh the mirror trick is quite handy. i don’t think i’ve heard that one before. i’ll keep that one in my back pocket in case i ever need it some day. i can’t remember exactly how i learned what they meant, but i think it was probably u for union and n for ntersection.
Math is my worst subject by far. This was incomprehensible to me at first, but I read it a few times and I started to kind of get it, so thank you for that.
In my mind, boolean operators meant things like AND/OR in internet searches. This functionality and using quotation marks to mean “these exact words” seem to no longer work on Google anyway.
Does anyone know how to make these work the way they used to? I used to be quite the “google-fu” master, but search has gone to total shit.
i also think the “etymology” of the boolean symbols is very helpful in remembering which is which. in lattice theory, their use was inspired by similar notation in set theory. so,
A ∨ Bis likeA ∪ B, whileA ∧ Bis likeA ∩ B.generally,
A ∨ Bis “the smallest thing that’s greater than or equal to both A and B”, whileA ∧ Bis “the biggest thing that’s less than or equal to both A and B”. similarly to howA ∪ Bis “the smallest set that contains both A and B”, whileA ∩ Bis “the largest set that’s contained in both A and B”. you can also take things a step further by saying that in the context of sets,A ≤ BmeansA ⊆ B. doing this means thatA ∨ B = A ∪ B, whileA ∧ B = A ∩ B. and from this perspective, the “sharp-edged” symbols (<,∧,∨) are just a generalization of their “curvy” counterparts (⊂,∩,∪).in the context of boolean algebra, you can set
False < True, which at first may seem a bit arbitrary, but it agrees with the convention the thatFalse = 0andTrue = 1, and it also makesA ∨ BandA ∧ Bhave the same meanings as described above.for some reason to remember ∩ and ∪ when I first learned it in school I visualized a mirrored symbol on top. the ∩ looked like a X which represented an intersection, while ∪ looked like an O which represented a whole. for English ∪ already looks like a U which can be thought of as short for union. that would’ve been easier.
ooh the mirror trick is quite handy. i don’t think i’ve heard that one before. i’ll keep that one in my back pocket in case i ever need it some day. i can’t remember exactly how i learned what they meant, but i think it was probably u for union and n for ntersection.
Math is my worst subject by far. This was incomprehensible to me at first, but I read it a few times and I started to kind of get it, so thank you for that.
In my mind, boolean operators meant things like AND/OR in internet searches. This functionality and using quotation marks to mean “these exact words” seem to no longer work on Google anyway.
Does anyone know how to make these work the way they used to? I used to be quite the “google-fu” master, but search has gone to total shit.