WRITING THE ELEMENTS OF GIVEN SETS FROM VENN DIAGRAM

Question 1 :

Using the adjacent Venn diagram, find the following sets:

(i) A - B (ii) B - C (iii) A' U B' (iv) A' n B' (v) (B U C)'

(vi) A − (B U C) (vii) A − (B n C)

Solution :

(i) A - B  =  {4, 6, 3}

(ii) B - C  =  {-1, 5, 7}

(iii) A' U B'

A'  =  {-3, 0, 1, 2, 5, 7, 8}

B'  =  {-3, 0, 1, 2, 3, 4, 6}

A' U B'  =  {-3, 0, 1, 2, 3, 4, 5, 6, 7, 8}

(iv) A' n B'

A' n B'  =  {-3, 0, 1, 2}

(v) (B U C)'

B U C  =  {-3, -,2, -1, 0, 3, 5, 7, 8}

(B U C)'  =  {4, 6, 1, 2}

(vi) A − (B U C)

A = {-2, -1, 3, 4, 6} and B U C  =  {-3, -,2, -1, 0, 3, 5, 7, 8}

A − (B U C)  =   {4, 6}

(vii) A − (B n C)

B n C  =  {-2, 8}

A  =  {-2, -1, 3, 4, 6}

A − (B n C)  =  {-1, 3, 4, 6}

Question 2 :

If K = {a, b, d, e, f}, L = {b, c, d, g} and M = {a, b, c, d, h}, then find the following :

(i) K U (L n M) (ii) K n (L U M) (iii) (K U L) n (K U M)

(iv) (K n L) U (K n M) and verify distributive laws.

Solution :

(i) K U (L n M)

(L n M)  =  { b, c, d }

K U (L n M)  =  {a, b, c, d, e, f}

(ii) K n (L U M)

(L U M)  =  {a, b, c, d, g, h} 

K n (L U M)  =  {a, b, d}

(iii) (K U L) n (K U M)

(K U L)  =  {a, b, c, d, e, f, g}

(K U M)  =  {a, b, c , d, e, f, h}

(K U L) n (K U M)  =  {a, b , c, d , e, f}

(iv) (K n L) U (K n M)

K = {a, b, d, e, f}, L = {b, c, d, g} and M = {a, b, c, d, h}

(K n L)  =  {b, d}

(K n M)  =  {a, b, d}

(K n L) U (K n M)  =  {a, b, d}

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