HOW TO WRITE ELEMENTS OF GIVEN SET FROM VENN DIAGRAM

Questions :

Using the given Venn diagram, write the elements of

(i) A (ii) B (iii) A∪B (iv) A∩B

(v) A–B (vi) B–A (vii) A′ (viii) B′

(ix) U

Solution :

(i)  We have to write the elements in the circle A.

A  =  {2, 4, 7, 8, 10}

(ii)  We have to write the elements in the circle B.

B  =  {3, 4, 6, 7, 9, 11}

(iii)  A U B means the elements in both circles.

A U B   =  {2, 3, 4, 6, 7, 8, 9, 10, 11}

(iv) A ∩ B means the common elements of both sets A and B.

A∩B  =  {4, 7}

(v) A – B 

A - B  =  {2, 8, 10}

(vi) B – A 

B - A  =  {3, 6, 9, 11}

(vii)  A'  =  {1, 3, 6, 9, 11, 12}

(viii)  B′  =  {1, 2, 8, 10, 12}

(ix)  U  =  {1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12}

(2)  Find A∪B, A∩B, A–B and B–A for the following sets.

(i) A  =  {2, 6, 10, 14} and B  =  {2, 5, 14, 16}

Solution :

AUB  =  {2, 4, 5, 6, 10, 14, 16}

A n B  =  {2, 14}

A - B  =  {6, 10}

B - A  =  {5, 16} 

(ii) A = {a, b, c, e, u} and B = {a, e, i, o, u}

Solution :

AUB  =  {a, b, c, e, i, o, u }

A n B  =  {a, e, u}

A - B  =  {b, c}

B - A  =  { i, o} 

(iii) A  =  {x : x ∈N, x ≤ 10} and B = {x : x ∈W, x < 6}

Solution :

A  =  {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

B  =  {0, 1, 2, 3, 4, 5}

AUB  =  {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A n B  =  { 1, 2, 3, 4, 5}

A - B  =  {6, 7, 8, 9, 10}

B - A  =  {0} 

(iv) A= Set of all letters in the word “mathematics” and

B = Set of all letters in the word “geometry”

Solution :

A = {m, a, t, h, e, i, c, s }

B =  {g, e, o, m, e, t, r, y}

AUB  =  {m, a, t, h, e, i, c, s, g, o,  r, y}

A n B  =  { m, t, e}

A - B  =  {a, h, i, c , s}

B - A  =  {g, o, r, y} 

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