Definition and Examples of Sets; Operations on Sets, Types of Sets

1. SETS AND
VENN
DIAGRAMS
DR. FARHANA SHAHEEN

3. Sets
A Set is a collection of well-defined and distinct objects.
Sets are denoted by capital letters A, B, C, etc.

6. Example:
Set of Polygons P
Square is a member of P
Circle is not a member of P

18. Example:01

26. Subset of a Set

31. Operations on Sets
Sets are treated as mathematical objects.
Similar to numbers, we can perform certain mathematical operations on sets.
Intersection: 𝐴 ∩ 𝐵 = {𝑥: 𝑥 ∈ 𝐴 𝒂𝒏𝒅 𝑥 ∈ 𝐵}
Union: A ∪ 𝐵 = {𝑥: 𝑥 ∈ 𝐴 𝒐𝒓 𝑥 ∈ 𝐵}
Complement of A = 𝐴′
= 𝐴𝑐
= {𝑥: 𝑥 ∉ 𝐴}
Difference: 𝐴B = {𝑥: 𝑥 ∈ 𝐴, 𝑏𝑢𝑡 𝑥 ∉ 𝐵}

34. 𝐴 ∩ 𝐵 = {𝑥: 𝑥 ∈ 𝐴 𝒂𝒏𝒅 𝑥 ∈ 𝐵}

36. Union and Intersection of two sets

37. 𝐴′
= 𝐴𝑐
= {𝑥: 𝑥 ∉ 𝐴}

38. Venn Diagram of complement of A
Universal set is the largest set.
Let A be a subset of U.
Then A’ is the complement of A, which
is the set of all elements which are Not
in A.

39. VENN
DIAGRAMS
UNION
INTERSECTION
COMPLEMENT
OF TWO SETS A and B

41. DISJOINT SETS
Two sets A and B are called disjoint when they have
nothing in common. The sets which are Not disjoint are called
Overlapping sets. Example:

42. Disjoint Sets

46. Example:02
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
T is the set of all multiples of 2
F is the set of all multiples of 4
Write T and F in Tabular form.
Find T’ and F’.
Draw the Venn Diagram.

47. Difference of two
sets
B−𝐴 = 𝑥: 𝑥 ∈ 𝐵 𝑎𝑛𝑑 𝑥 ∉ 𝐴
A−𝐵 = 𝑥: 𝑥 ∈ 𝐴 𝑎𝑛𝑑 𝑥 ∉ 𝐵
Note that
A − B ≠ 𝐵 − 𝐴

49. Example: 03

50. https://www.slideshare.net/AdilAslam4/basic-of-sets-notes-set-theory