Question

If

Solve the following problems and draw Venn diagrams for each of them.

Answer 1

X = {2, 3, 4, 5, 6}

Y = {1, 7, 8}

Z = {1, 3, 5, 7, 9}

(1) X ∪ Y = {2, 3, 4, 5, 6} ∪ {1, 7, 8}

= {1, 2, 3, 4, 5, 6, 7, 8}

And the Venn diagram is:

(2) Y ∪ Z = {1, 7, 8} ∪ {1, 3, 5, 7, 9}

= {1, 3, 5, 7, 8, 9}

And the Venn diagram is:

(3) X ∪ Z = {2, 3, 4, 5, 6} ∪ {1, 3, 5, 7, 9}

= {1, 2, 3, 4, 5, 6, 7, 9}

And the Venn diagram is:

(4) (X ∪ Y) ∪ Z = {1, 2, 3, 4, 5, 6, 7, 8} ∪ {1, 3, 5, 7, 9}

(From (1) X ∪ Y = {1, 2, 3, 4, 5, 6, 7, 8} )

= {1, 2, 3, 4, 5, 6, 7, 8, 9}

And the Venn diagram is:

(5) X ∪ (Y ∪ Z) = {2, 3, 4, 5, 6} ∪ {1, 3, 5, 7, 8, 9}

(From (2) Y ∪ Z = {1, 3, 5, 7, 8, 9})

= {1, 2, 3, 4, 5, 6, 7, 8, 9}

And the Venn diagram is: