Question

construct a venn diagram illustrating the sets below.
$u=\\{a, b, c, d, e, f, g, h, i\\}$
$w=\\{a, b, c, e, f\\}$
$x=\\{d, e, f, h\\}$
$z=\\{c, d, e, i\\}$

Explanation:

Step1: Identify unique elements of W

Elements only in $W$: $a, b$ (not in $X$ or $Z$)

Step2: Identify unique elements of X

Elements only in $X$: $h$ (not in $W$ or $Z$)

Step3: Identify unique elements of Z

Elements only in $Z$: $i$ (not in $W$ or $X$)

Step4: Find W∩X only

Elements in $W$ and $X$, not $Z$: $f$

Step5: Find W∩Z only

Elements in $W$ and $Z$, not $X$: $c$

Step6: Find X∩Z only

Elements in $X$ and $Z$, not $W$: $d$

Step7: Find W∩X∩Z

Element in all three sets: $e$

Step8: Find U outside all sets

Element in $U$, not in $W,X,Z$: $g$

Answer:

• Region only in circle $W$: $a, b$
• Region only in circle $X$: $h$
• Region only in circle $Z$: $i$
• Region in $W \cap X$ only: $f$
• Region in $W \cap Z$ only: $c$
• Region in $X \cap Z$ only: $d$
• Region in $W \cap X \cap Z$: $e$
• Region in $U$ outside all circles: $g$

(When placing on the Venn diagram:

1. Put $a,b$ in the red circle ($W$) area that does not overlap with other circles
2. Put $h$ in the blue circle ($X$) area that does not overlap with other circles
3. Put $i$ in the purple circle ($Z$) area that does not overlap with other circles
4. Put $f$ in the overlapping area of red ($W$) and blue ($X$) circles only
5. Put $c$ in the overlapping area of red ($W$) and purple ($Z$) circles only
6. Put $d$ in the overlapping area of blue ($X$) and purple ($Z$) circles only
7. Put $e$ in the triple overlap of all three circles
8. Put $g$ in the outer area of the green rectangle ($U$), outside all three circles)