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By the end of the lesson students should be able to:
Define a Venn Diagram.
Explain its components and purpose.
Create a Venn Diagram correctly.
Recognize relationships among concepts.
A Venn Diagram uses overlapping circles or shapes to illustrate logical relationships between two or more sets of items.
Universal Set: U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Subset S = {0, 1, 2}, Subset T = {0, 1, 2, 3, 4}
S ⊆ U and T ⊆ U (elements of S and T are in U).
S ⊆ T (all elements of S are in T).
Representation: Smaller circle (S) is enclosed in the larger circle (T).
Enclosed in a rectangle representing the universal set U.
The intersection of two sets A and B, denoted as A ∩ B, comprises elements common to both sets.
Represented in a Venn diagram by overlapping regions.
Let M = {vowels in the alphabet}, L = {letters in ‘algebra’}.
M = {a, e, i, o, u}, L = {a, l, g, e, b, r}.
Intersection: M ∩ L = {a, e}.
The union of A and B, denoted as A U B, is the set containing elements in either A or B or both.
Illustrated by the shaded portion of the circles in a Venn Diagram.
For sets M and L defined above:
M U L = {a, e, i, o, u, l, g, b, r}.
The complement of a set A, denoted A’, includes elements in the universal set U not contained in A.
Corresponds to the shaded region outside set A in a Venn Diagram.
If U = {days of the week}, and B = {days not included on weekdays}:
B’ = {Monday, Tuesday, Wednesday, Thursday, Friday}.
Two sets are disjoint if they have no elements in common; their intersection is an empty set ({}).
Let A = {2, 4, 6, 8}, B = {1, 3, 5, 7, 9}.
No elements shared; thus A and B are disjoint.
For sets A, B, C, solve:
A ∩ (B U C)
(A’ ∩ B) U C
Given regions represented by Roman numerals, identify items within each region.
Survey of 100 people regarding visits to Tagaytay and Baguio and calculate individual and combined visits.
Venn diagram analysis of 500 investors in real estate and forex trading and determine subsets.
Survey of 62 students liking at least one of apples, bananas, or oranges; analyze preferences and exclusives.
Assess understanding of the topic with options ranging from none to a lot.