To find the value of x and n(A), we can use the formula:
n(AUB) = n(A) + n(B) - n(ANB)
We are given that n(U) = 80, n(A) = 3x - 2, n(B) = 3x, n(AUB) = x, and n(ANB) = 5. Substituting these values into the formula above, we get:
x = (3x - 2) + 3x - 5
Simplifying this equation, we get:
x = 6x - 7
Rearranging this equation, we get:
5x = 7
x = 7/5
Therefore, x = 1.4.
To find n(A), we can use the formula:
n(A) = n(AUB) + n(ANB) - n(B)
Substituting the values we know, we get:
n(A) = x + 5 - 3x
Simplifying this equation using the value of x we found above, we get:
n(A) = 1.4 + 5 - 4.2
n(A) = 2.2
Therefore, n(A) = 2.2.
To draw the Venn diagram, we can start by drawing a rectangle to represent the universal set U, and then draw two overlapping circles inside the rectangle to represent sets A and B. We can label the intersection of the circles with the number 5, to represent n(ANB). We can label the number x inside the circle for A to represent n(AUB), and we can label the circle for B with the number 3x to represent n(B). We can then use the formulas above to find the values of x and n(A) and label the appropriate areas in the Venn diagram.