VerifiedHint: You need to solve this question by understanding the meaning of union of two sets. You also need to use the data that there are a total of three sets present while drawing the Venn diagram.
Complete step-by-step answer:
Before we start with the solution, let us understand the meaning of different symbols and terms used in the question.
Universal set: The set containing all objects or elements and of which all other sets are subsets. So, for our question the universal set is the union of the three sets A, B, and C.
Union: The union (denoted by $\cup $ ) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other.
Intersection: The intersection of two sets has only the elements common to both sets. If an element is in just one set, it is not part of the intersection. The symbol is an upside down $\cap $ .
Now, let us start with the actual solution to the question given above.
We know that for the above question the universal set is the union of the sets A, B, and C. So, the universal set can be represented in form of Venn diagram as:
Now we are asked to draw a Venn diagram for $B\cup C$ . If we interpret it, we are asked to shade that region from the universal set, which is the part of set B or set C or both of them. So, the final Venn diagram comes out to be:
Therefore, the region shaded with blue represents the set given by $B\cup C$ .
Note: Be careful while drawing the universal set, the general mistake students make is when they are asked to draw $B\cup C$ , they draw the two circles B and C and forget about the other sets leading to the wrong Venn diagram. Also, be careful about the symbols of union and intersection, as they might be confusing.
