DRAWING VENN DIAGRAM FOR THE GIVEN STATEMENT

Question 1 :

Using the set symbols, write down the expressions for the shaded region in the following

(i)  

Solution :

In the circle Y, the common area of both X and Y are neglected. Hence it is the venn diagram of Y'. 

(ii)  

Solution :

They have shaded the area by neglecting the circles X and Y. Hence the venn diagram represents the statement (X U Y)'.

(iii)  

Solution :

The shaded portion of first circle can be denoted as X' and the shaded region of the second circle can be denoted as Y'. Hence the statement for the given venn diagram is X' U Y'.

Question 2 :

Let A and B be two overlapping sets and the universal set be U. Draw appropriate Venn diagram for each of the following,

(i) A∪B (ii) A∩B (iii) (A∩B)′ (iv) (B–A)′ (v) A′∪B′ (vi) A′∩B′

(vii) What do you observe from the Venn diagram (iii) and (v)?

Solution :

(i) A U B

(ii) A ∩ B

(iii) (A∩B)′

(iv) (B – A)′

(v) A′ ∪ B′

(vi) A′ ∩ B′

(vii) What do you observe from the Venn diagram (iii) and (v)?

(iii) and (v) are equal.

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