Q. 54.4( 119 Votes )

Draw approp

Answer :

(i) (A ∪ B)’

First we draw (A
B)

Yellow region is (A B).


The shaded region represents (A B).


We have to draw diagram for complement of (A B) i.e.(A ∪ B)’, which is given by U - (A B).

Green region is (A ∪ B)’.



(ii) A’ ∩ B’

Here we have to draw diagram of (A’
B’)


So, first we draw A’( = U - A)



Now, we draw B’( = U - B)



Now the area common in both the shaded regions gives us (A’ B’)



Here, we observe that the final result for (i) and (ii) is same.


(A B)’ = (A’ B’)


(iii) (A ∩ B)’

First we draw (A
B)



The shaded region represents (A B).


We have to draw diagram for complement of (A B) i.e.(A ∩ B)’ , which is given by U - (A B)



(iv) A’ ∪ B’


Here we have to draw diagram of (A’
B’)


So, first we draw A’( = U - A)



Now, we draw B’( = U - B)



Now the area present in both is added to give (A’ B’)



Here, we observe that the final result for (iii) and (iv) is same.


(A B)’ = (A’ B’)

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