To represent the information on a Venn diagram, we can begin by drawing two overlapping circles to represent the two businesses: fishmongers and petty traders.
a) Venn diagram representation:
Let's label one circle as "Fishmongers" and the other as "Petty Traders."
Now, according to the given information:
- There are a total of 74 women in the community.
- 6 women are both fishmongers and petty traders.
We can place these 6 women in the overlapping region of the two circles.
- The number of women who are only petty traders is three more than twice the number of women who are involved in any of the two businesses.
Let's say x represents the number of women who are involved in any of the two businesses. Then, three more than twice that number is (3 + 2x).
So, we can place "x" in the region that represents women involved in any of the two businesses and "3 + 2x" in the region that represents women who are only petty traders.
b) Now, to find the number of women who are:
I) Fishmongers:
From the diagram, you can see that there are 6 women in the overlapping region representing fishmongers and petty traders, giving us the answer of 6.
ii) Petty traders:
From the diagram, you can see that there are "3 + 2x" women in the region that represents women who are only petty traders. Therefore, the number of women who are petty traders is "3 + 2x".