
Let A and B be the two sets such that , and then draw a Venn diagram to illustrate this information. If then find
(a) The value of
(b)
Answer
496.2k+ views
Hint: We solve this problem by using the Venn diagrams of sets. The Venn diagrams represent the diagrammatic representation of sets inside the universal set
For solving the first part we use the given condition along with the formulas of sets that is
For solving second part we use the general formula of sets that is
Complete step-by-step solution
We are given that , and
Let us draw a Venn diagram that represents the given information then we get
(a) The value of
We are given that
We know that the formulas of sets that is
By using the above formulas to equation (i) we get
By substituting the required values in above equation we get
Therefore, the value of is 12
(b)
We know that the direct formula of union of sets that is
By substituting the required values from the formulas we used before in above equation we get
Now by substituting the required values in terms of in above equation we get
Now, by substituting in above equation we get
Therefore the value of is 200.
Note: Students may make mistakes in the Venn diagram representation.
Venn diagrams are the diagrammatic representation of sets in the universal set
So the Venn diagram must be drawn as
But students may miss the universal set and draw the Venn diagram as
This will be the wrong representation because all the sets are subsets of a universal set which is very important to represent in the Venn diagram.
For solving the first part we use the given condition
For solving second part we use the general formula of sets that is
Complete step-by-step solution
We are given that
Let us draw a Venn diagram that represents the given information then we get

(a) The value of
We are given that
We know that the formulas of sets that is
By using the above formulas to equation (i) we get
By substituting the required values in above equation we get
Therefore, the value of
(b)
We know that the direct formula of union of sets that is
By substituting the required values from the formulas we used before in above equation we get
Now by substituting the required values in terms of
Now, by substituting
Therefore the value of
Note: Students may make mistakes in the Venn diagram representation.
Venn diagrams are the diagrammatic representation of sets in the universal set
So the Venn diagram must be drawn as

But students may miss the universal set

This will be the wrong representation because all the sets are subsets of a universal set
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