Question

construct a venn diagram illustrating the sets below.
$u = {1, 2, 3, 4, 5, 6, 7, 8, 9}$
$w={1, 3, 4, 7, 9}$
$y = {1, 2, 3, 4, 5}$
$z={1, 5, 8, 9}$

Explanation:

Step1: Find the intersection of all sets

$W\cap Y\cap Z = \{1\}$, so place 1 in the region where all three circles (W, Y, Z) overlap.

Step2: Find $W\cap Y$

$W\cap Y=\{1,3,4\}$, since 1 is already in the triple - intersection, place 3 and 4 in the region where only W and Y overlap.

Step3: Find $W\cap Z$

$W\cap Z = \{1,9\}$, since 1 is already accounted for, place 9 in the region where only W and Z overlap.

Step4: Find $Y\cap Z$

$Y\cap Z=\{1,5\}$, since 1 is already in the triple - intersection, place 5 in the region where only Y and Z overlap.

Step5: Find elements only in W

Elements only in $W$ are $\{7\}$, place 7 in the non - overlapping part of circle W.

Step6: Find elements only in Y

Elements only in $Y$ are $\{2\}$, place 2 in the non - overlapping part of circle Y.

Step7: Find elements only in Z

Elements only in $Z$ are $\{8\}$, place 8 in the non - overlapping part of circle Z.

Step8: Find elements in the universal set but not in W, Y or Z

Elements in $U$ but not in $W\cup Y\cup Z$ are $\{6\}$, place 6 outside all the three circles but inside the rectangle representing the universal set $U$.

Answer:

The Venn - diagram should have three overlapping circles labeled W, Y, and Z inside a rectangle labeled U. The number 1 should be in the region where all three circles overlap. The numbers 3 and 4 should be in the region where only W and Y overlap. The number 9 should be in the region where only W and Z overlap. The number 5 should be in the region where only Y and Z overlap. The number 7 should be in the non - overlapping part of circle W. The number 2 should be in the non - overlapping part of circle Y. The number 8 should be in the non - overlapping part of circle Z. The number 6 should be outside all the three circles but inside the rectangle representing U.