MATHM | Sets

• In mathematics is a collection of well defined and distinct objects, considered as an object in its own right.

  Sets
• are one of the most fundamental concepts in mathematics.

  Sets
• Name of Sets are represented by capital letters
• Separated by commas
• The object that belong inside a set are elements
• Elements can be represented by listing it between braces ● Example: A= {a, e, i, o, u}
• Tells how many things are in a set

  Cardinality
• Repeating objects or elements should be counted as 1 only
• The totality of all the elements in a two or more given sets

  Universal Set
• Denoted by “U”

  Universal Set
• Example: A={2, 4, 6, 8} B={1, 2, 3, 4} U={1, 2, 3, 4, 6,8}

  Universal Set
• • has no elements Its
  • Its cardinality number is zero

  Null Set
• Example: { }

  Null Set
• - Combination of elements of two or more sets - Denoted by “U”

  Union Set
• Example: A= {1, 4, 5} B= {1, 2, 3} AUB = {1, 2, 3, 4, 5,}

  Union Set
• - Refers to the similar elements of two or more sets - Denoted by “∩”

  Intersection of set
• - Refers to elements of first set alone but not an

  element of other set

  - Denoted by “-”

  Difference of Set
• Example: Find A-B and B-A A= {1, 4, 5, 6} B= {1, 2, 3, 5,} A-B= {4} B-A= {2, 3}

  Difference
• - Refers to the elements of the universal set alone

  which is not part of the

  concerned set.

  - Denoted by ‘ (apostrophe)

  Complement of Set
• Example: U={a, b, c, d, e, f, g, h, i, j} A={a, e, i} A’ ={b, c, d, f, g, h, j}

  Complement
• "⊆"

  is a subset of (equally the same)
• "⊂"

  is a proper subset of
• Sets are ___ if they have exactly the same elements

  Equal sets
• Example: M={1,3,9,5,−7} N={5,−7,3,1,9} therefore M=N

  Equal
• Sets are equivalent if they have exactly the same number of elements

  Equivalent Set
• Example: A= {1, 4, 5} B= {1, 2, 3, 5} AB= {1,5}

  Intersection
• Example: S={1,2,3} T={a,b,c} therefore S∼T

  Equivalent