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Relations, functions and equivalence

Relations as sets of pairs; reflexive, symmetric, transitive; functions and bijections.

A relation is a set of ordered pairs; an equivalence relation (reflexive, symmetric, transitive) partitions its set into classes; a function is a relation with exactly one output per input. Picture it: "same remainder mod 3" splits the integers into three columns. Think it: a bijection is how we say two sets have the same size, including infinite ones.

ຕົວຢ່າງທີ່ໄດ້ເຮັດ · truth table of p implies q

Discrete-Math · Propositional-Logic

Truth table of p implies q

ຂັ້ນຕອນຕໍ່ຂັ້ນຕອນ

p \Rightarrow q
2 variable(s) → 4 rows. Fill in every combination.
\
Contingent: true for some inputs, false for others.

ເປີດເຜີຍຄຳຕອບ

p \Rightarrow q

ປັດຈຸບັນທ່ານ ເລືອກບັນຫາ ຫຼື ພິມ ຫຼື ແຕ້ມເອງ. ທຸກບາດກ້າວ, ຮູບ, ຄໍາຕອບຖືກລົບຈົນກວ່າເຈົ້າຈະຖາມມັນ.

ຮັກສາການເຮັດວຽກຂອງທ່ານໄວ້

ບັນຊີຟຣີ ເພີ່ມຂໍ້ມູນໃສ່ບົດຮຽນທຸກບົດ, ບັນທຶກຂອງສິ່ງທີ່ທ່ານໄດ້ເຮັດແລ້ວ, ບັນຫາທີ່ທ່ານໄດ້ແກ້ໄຂໄວ້ໃນບ່ອນດຽວ ແລະ ຄູສອນທີ່ທ່ານສາມາດຖາມກ່ຽວກັບໜ້ານີ້. ຄະນິດສາດເອງແມ່ນເປີດໃຫ້ທຸກຄົນ, ບໍ່ວ່າຈະໄດ້ເຂົ້າສູ່ລະບົບ ຫຼື ບໍ່.

ລົງທະບຽນ ចូល

ຕົວສະແດງທີ່ໃຊ້ຢູ່ທີ່ນີ້

ກົດຕົວອັກສອນໃດໜຶ່ງເພື່ອເບິ່ງຄວາມໝາຍເຕັມ, ຮູບ ແລະ ຕົວອັກສອນແຕ່ລະຕົວໃນມັນໝາຍຄວາມວ່າແນວໃດ.

ວິທີການ: Relations, functions and equivalence

2 variable(s) → 4 rows. Fill in every combination.
Contingent: true for some inputs, false for others.

ຄໍາຖາມທີ່ຄົນຖາມ

Are some infinities bigger than others?

Yes. The integers and the rationals can be listed; the real numbers cannot (Cantor's diagonal argument), so there are strictly more reals than integers.

What is the difference between a relation and a function?

A relation pairs inputs with outputs freely; a function is a relation in which every input gets exactly one output.

ເພີ່ມເຕີມໃນ Set Theory & Logic

Sets and operations Cardinality and infinity Logic and methods of proof