Given U={while numbers from 1-20}, A={factors of 12}, B={factors of 15} and C={factors of 18}, find: AnB, AUB, A', B', (AUB)'

Question

Please illustrate a Venn diagram

Answer 1

A= {1,2,3,4,6,12}

B = {1,3,5,15}

C = {1,2,3,5,9,18}   ⇐ won't be needed in your problem

 

A∩B = {1,3}  ⇐ Intersection, i.e. elements found in both sets *

 

A∪B = {1,2,3,4,5,6,12,15}  ⇐ elements found in either A or B, or both #

 

A' = {5,7,8,9,10,11}   ⇐ elements of universal set excluded from A

 

B' ⇐ You can try this!      

(A∪B)' means "those elements excluded from A∪B (but also in universal set)...you can try this, too.

 

As for the Venn diagram, draw a (biggish) rectangle and place 3 semi-overlapping circles in it, labeled A & B.

* the numbers 1 & 3 are placed in the overlapping area of circles A & B.

The numbers not in either A or B are placed outside the figure8 formed by the two circles.

Inside A but not in the overlapped circles you put the rest of the numbers in the # list, etc.

When all is done, you'll have twenty numbers in the rectangle, distributed appropriately into four distinct parts of the diagram: overlap of circles, non-overlap of A, non-overlap of B, and outside of both circles.