Question

If two sets are disjoint, then what region represents the union of their complements in a Venn diagram?

Answer 1

If 2 sets are disjoint means they have not any common element.

Draw a rectangle & inscribe inside this rectangle 2 circles that do not intersect.

cercle₁ ∩ cercle₂ =Ф.
Their complement would be the part of the rectangle - the 2 circles

Answer 2

Answer: The union of the complements is equal to the universal set, this is the whole region in the Venn diagram.

Explanation:

Two sets are disjoint if they do not share any element, so if the sets are A and B we would have that:

A∩B = {∅}

the intersection between two disjoint sets is equal to the empty set.

now, as they are disjoint, we will have that the complement of A ; Ac, contains all the values of B (and all the other things that do not belong to A), and the complement of B, Bc contains all the components of A (and all the other elements thta do not belong to B).

Then when we calculate Ac∪Bc we are including:

All the values of B

All the values that are not in A

All the values of A

All the values that are not in B.

So the union of the complements is the universal set (the whole Venn diagram)