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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.

ಕಾರ್ಯಗತಗೊಂಡ ಮಾದರಿ · truth table of p implies q

Discrete-Math · Propositional-Logic

Truth table of p implies q

ಅಡಿಯಿಡು (step)

  1. p \Rightarrow q

    2 variable(s) → 4 rows. Fill in every combination.

  2. \

    Contingent: true for some inputs, false for others.

ಉತ್ತರವನ್ನು ತಿಳಿಸಿ
p \Rightarrow q

ಈಗ ನೀವು ಪ್ರತಿಯೊಂದು ಹೆಜ್ಜೆಯಲ್ಲಿ, ಒಂದು ಚಿತ್ರವನ್ನು ನೀವು ಕೇಳುವ ತನಕ ಅಡಗಿಸಿಟ್ಟಿಡಿರಿ.

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ಮೇಲೆ ಗುರುತು ಹಾಕು ಪ್ರವೇಶ (ಲಾಗಿನ್)

ಇಲ್ಲಿ ಬಳಸಲಾದ ಸಂಕೇತಗಳು

ಈ ವಚನದಲ್ಲಿ ಬಳಸಲಾಗಿರುವ ಗ್ರೀಕ್‌ ಪದವು, ಚಿತ್ರ ಮತ್ತು ಚಿತ್ರಗಳನ್ನು ನೀವು ಸುಲಭವಾಗಿ ಅರ್ಥಮಾಡಿಕೊಳ್ಳಲು ಸಹಾಯ ಮಾಡುತ್ತದೆ.

ಹೇಗೆ: Relations, functions and equivalence

  1. 2 variable(s) → 4 rows. Fill in every combination.
  2. Contingent: true for some inputs, false for others.

ಜನರು ಕೇಳುವುದು

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.

ಇನ್ನಷ್ಟು Set Theory & Logic

Sets and operationsCardinality and infinityLogic and methods of proof