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If n(U)= 80, n(A) = 3x-2, n (B) = 3x, n(AUB) = x and n(ANB) = 5, then by

drawing a Venn diagram, and find
(i) the value of x.
(ii) the value of n(A).

1 Answer

1 vote

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.

User Arkadiusm
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