Question

construct a venn diagram illustrating the sets below.
u = {a, b, c, d, e, f, g, h, i}
y = {d, f, h}
z = {c, e, f, g, h, i}
these buttons change the venn diagram.

Explanation:

Step1: Identify Y-only elements

Elements in $Y$ not in $Z$: $Y - Z = \{d, f, h\} - \{c, e, f, g, h, i\} = \{d, h\}$

Step2: Identify intersection elements

Elements in both $Y$ and $Z$: $Y \cap Z = \{d, f, h\} \cap \{c, e, f, g, h, i\} = \{f\}$

Step3: Identify Z-only elements

Elements in $Z$ not in $Y$: $Z - Y = \{c, e, f, g, h, i\} - \{d, f, h\} = \{c, e, g, i\}$

Step4: Identify universal set leftovers

Elements in $U$ not in $Y$ or $Z$: $U - (Y \cup Z) = \{a, b, c, d, e, f, g, h, i\} - \{c, d, e, f, g, h, i\} = \{a, b\}$

Step5: Map to Venn diagram

Place $\{d, h\}$ in the red circle only, $\{f\}$ in the overlap, $\{c, e, g, i\}$ in the blue circle only, and $\{a, b\}$ in the outer area of the universal set box.

Answer:

A Venn diagram with:

1. Region only in Y: $\{d, h\}$
2. Intersection of Y and Z: $\{f\}$
3. Region only in Z: $\{c, e, g, i\}$
4. Region in U but not Y/Z: $\{a, b\}$