In this section, you will learn, how to draw a venn diagram for A union B whole complement.
Venn Diagram of (A u B)' :
To represent (A u B)' in venn diagram, we have to shade the region other than A and B.
First draw Venn diagram for (A u B) and then (A u B)'.
Demorgan's law for (A u B)'.
(A u B)' = A' n B'
Lets draw the Venn diagram of (A' n B') and verify the above Demorgan's law.
We have already drawn venn diagram for (A u B)'.
Now, let's draw Venn diagram for (A' n B').
Draw Venn diagram for A' and B'.
Then, to draw Venn diagram for (A' n B'), find the common region of A' and B'.
The resulting Venn diagrams of (A u B)' and (A' n B') are same.
So,
(A u B)' = A' n B'
Problem 1 :
Use the Venn diagram to answer the following questions
(i) List the elements of U, E', F', (E U F)' and (E n F)'
Solution :
(i) To find the elements of universal set U, we have to list out all the elements that we find in the rectangular box.
U = { 1, 2, 3, 4, 7, 9, 10, 11 }
(ii) To find the elements of the set E', we have to list out all the elements other than the circle E.
E' = { 3, 9, 10, 11 }
(iii) To find the elements of the set F', we have to list out all the elements other than the circle F.
F' = { 1, 2, 3, 4, 7, 10 }
(iv) To find the elements of the set (E U F)', first we have to find the the elements of the set E U F
E U F = { 1, 2, 3, 4, 7, 9, 10, 11 }
(E U F)' = { }
(v) To find the elements of the set (E n F)', first we have to find the the elements of the set E n F
E n F = { 4, 7 }
(E n F)' = { 1, 2, 3, 9, 10, 11 }
Problem 2 :
If U = {x : 1 ≤ x ≤ 10, x ∊ N}, A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 9, 10}, find
(i) A' (ii) B' (iii) A' U B' (iv) A' ⋂ B'
Solution :
U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
A = {1, 3, 5, 7, 9}
B = {2, 3, 5, 9, 10}
(i) A' = { 2, 4, 6, 8, 10}
(ii) B' = { 1, 4, 6, 7, 8}
(iii) A' U B' = { 1, 2, 4, 6, 7, 8, 10 }
(iv) A' ⋂ B' = { 4, 6, 8 }
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