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Sets with Venn Diagrams – Examples

Let’s see 3 examples of sets with Venn diagrams. We will use examples of 3 sets, the set A, the set B and the set C and our base figure with which we will represent the examples of sets with venn diagrams is the next:

venn-diagram-base-1
Base figure

First example of sets with Venn diagrams

Our first example of sets is: A \cap (B \cup C)^{\text {C}}

Let’s start with the parentheses, we will take B and graphically represent how it would looks in a Venn diagram:

venn-diagram-1-b

Set B

Graphically represent the set C:

venn-diagram-1-c

Set C

We made the union of the set B with the set C. (B \cup C):

venn-diagram-1-b-c

(B \cup C)

Then the complement that has the parentheses was made. (B \cup C)^{\text{C}}

venn-diagram-1-b-cc

(B \cup C)^{\text{C}}

Then we graph the area that occupies only the set A to have it more visually:

venn-diagram-1-a

Set A

Finally, the intersection indicated in the example was made, so the answer is:

venn-diagram-1-ac

A \cap (B \cup C)^{\text{C}}

Second example of Venn diagrams

Our second example is: C \cup (A^{\text{C}}\cap A)

Now, as we did in the previous example, we start with what is inside the parentheses, identifying each area that says the example statement.

We draw the set A:

venn-diagram-2-a

Set A

The A complement would looks like this:

venn-diagram-2-ac

A^{\text{C}}

Then the intersection (A^{\text{C}} \cap A) was made:

(A^{\text{C}} \cap A)

Than the set C was drawn:

venn-diagram-2-c

Set C

And finally to arrive at the result, the union of C was made with (A^{\text{C}} \cap A), which was observed that the result is the same set of C:

venn-diagram-2-c

C \cup (A^{\text{C}} \cap A)

Third example with Venn diagrams

The third example of sets with Venn diagrams is: (A - B) \cap (C \cup B^{\text{C}})

Beginning with the resolution of the exercise, the A and B sets were first drawn:

And then the difference A - B was made:

venn-diagram-3-result

A-B

After proceeding to make the inside of the other parenthesis, first drawing the set C and then the complement of the set B:

Finally, to arrive at the result, the intersection that says the example was made, the result would be:

venn-diagram-3-result

(A - B) \cap (C \cup B^{\text{C}})

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