Maths(一)---Sets and Numbers(1)

Sets =

A set is a collection of objects called “elements” or “members” of the set.

Equality of Sets=

即係2個set含有相同元素.
比如,Let A = {a, e, i, o, u}, B = {u, o, i, e, a} andC = {a, a, e, i, i, o, u}
then A = B = C

Universal Set=

contains all the objects under consideration

Universal Set=

A set which contains no elements.Denoted by∅ or { }.

Subsets=

A⊂ B read as “A is a subset of B” or
B ⊃ A read as “B contains A”.

比如.Let A = {1, 3, 5} and B = {1, 2, 3, 4, 5}
then A ⊂ B or B ⊄ A

Disjoint Sets=

If sets A and B have no elements in common, then we say that A and B are disjoint,如
Let A = {1, 3, 5, 7} and B = {2, 4, 6, 7}then A and B are not disjoint since 7 is in both sets.i.e.7∈Aand7∈B.

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Set Operations

Union, ∪

ie. A ∪ B ={x : x ∈ A or x ∈ B}

例一.Let A = {a, b, c}, B = {1, 2, 3} and C = {a, c, e, 1, 3, 5},
then A ∪ B = {a, b, c, 1, 2, 3}
B ∪ C = {1, 2, 3, a, c, e, 5}
C ∪ A = {a, c, e, 1, 3, 5, b}



Intersection, ∩


ie.A ∩ B ={x : x ∈ A and x ∈ B}
例一.Let A = {a, b, c, d, e}, B = {c, d, e, f, g} andC = {a, e, i, o, u},
then A ∩ B = {c, d, e}
B ∩ C = {e}
C ∩ A = {a,e}




Difference \

ie.A \ B ={x : x ∈ A, x ∉ B}

例一.
Let S = {a, b, c, d} and T = {c, d, e, f},
then S \ T = {a, b}
T \ S = {e, f}




Complement, A─

A- ={x : x ∈U, x ∉ A}
例一.Let the universal set U be the English alphabet andA = {a, b, c, x, y, z}then A = {d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w}