It is given that

G = {apple, orange, banana, grape, durian, pear}

and

H = {apple, banana, grape, strawberry}.

(i) Draw a Venn diagram to represent the sets G and H.

(ii) From the Venn diagram, list all the elements in G ∪ H in set notation.

To represent sets G and H in a Venn diagram, we overlap the common elements apple, banana, and grape. The union of both sets is G ∪ H = {apple, orange, banana, grape, durian, pear, strawberry}. Each element is included once regardless of which set it belongs to, resulting in a comprehensive list of unique items from both sets.
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Answered by Anonymous | 2025-07-04

To solve the given question regarding sets G and H, let's go through each part step-by-step.
(i) Venn Diagram Representation
For the two sets G and H given as follows:

G = {\text{apple, orange, banana, grape, durian, pear}}
H = {\text{apple, banana, grape, strawberry}}

We will draw two overlapping circles to represent these sets, since they have some common elements.

Draw two circles that overlap. Label the first circle 'G' and the second circle 'H'.
Place the common elements of the sets (apple, banana, grape) in the overlapping area.
Place the elements unique to set G (orange, durian, pear) in the non-overlapping part of circle G.
Place the element unique to set H (strawberry) in the non-overlapping part of circle H.

Your Venn Diagram should look like this:
G --------------- | apple | | banana | | grape | | --------- | | | H | | | - | | | | ---------------- | orange | |durian | |pear |

| | strawberry -----------------
(ii) List All Elements in G \cup H
The union of sets G and H, denoted as G \cup H, is the set of all distinct elements that are in either set G, set H, or both. So we will gather all elements from both circles:
G \cup H = {\text{apple, orange, banana, grape, durian, pear, strawberry}}
This is your solution to the question.

Answered by LiamAlexanderSmith | 2025-07-06