ALGEBRA

• Set theory:

  cardinality

  |A| = number of elements
• SET THEORY

  subset - all elem of set a is an elem of set b

  proper subset (c) - some elem (not all) of set a, is an elem of set b

  Note.

  C = 5, 4, 3

  B= 1, 2, 3, 4, 5

  C (subset) B

  C < B

  signs face to greater cardinality

  superset (opposite of subset) - all elem of set a or more is an elem of another set

  proper superset (opposite of prop subset) - all elem of other set and more

  NOTE.

  B= 1 2 3 4 5

  C= 5 4 3

  B (superset) C

  B>C
• SET THEORY:

  CARDINALITY

  = (same number and same elems)

  ~ (same number not same elem)
• SET THEORY:

  EMPTY SET - no elements, is a subset of any set
• SET THEORY:

  UNION AND INTERSECTION

  UNION (U) - all elements, both separate and shared

  INTERSECTION (N)- only elements shared

  DIFFERENCE (-) - elem in set a that is not in set b. “only”
• SET THEORY:

  complement (A’) - outside set. “neither”

  universal set - all involve