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: Draw universal set

Draw a rectangle to represent the universal set \(U=\{a, b, c, d, e, f, g, h, i\}\).

Step2: Draw set Y

Draw a circle inside the rectangle to represent set \(Y = \{d,f,h\}\). Place the elements \(d\), \(f\), \(h\) inside this circle.

Step3: Draw set Z

Draw another circle that intersects the circle of \(Y\) to represent set \(Z=\{c,e,f,g,h,i\}\). Place the common elements \(f\), \(h\) in the intersection of the two - circles. Place the non - common elements of \(Z\) (\(c\), \(e\), \(g\), \(i\)) inside the circle of \(Z\) but outside the intersection.

Step4: Place remaining elements

Place the elements \(a\) and \(b\) inside the rectangle (universal set) but outside both circles of \(Y\) and \(Z\).

Answer:

A Venn diagram with a rectangle representing \(U\), a red - colored circle representing \(Y\) with elements \(d\), \(f\), \(h\) inside it, a blue - colored circle representing \(Z\) with elements \(c\), \(e\), \(f\), \(g\), \(h\), \(i\) inside it (where \(f\) and \(h\) are in the intersection of \(Y\) and \(Z\)), and elements \(a\) and \(b\) inside the rectangle but outside both circles.