# SETS – EXERCISE 1.4.4 – Class 9

1. Find union of A and B and represent it using venn diagram.

(i) A = {1, 2, 3, 4, 8, 9}, B = {1, 2, 3, 5}

(ii) A = {1, 2, 3, 4, 5}, B = {4, 5, 7, 9}

(iii) A = {1,2,3}, B = {4, 5, 6}

(iv) A = {1, 2, 3, ,4 ,5}, B = {1, 3, 5}

(v) A = {a, b, c, d}, B = {b, d, e, f}

Solution:

(i) A U B = {1, 2, 3, 4, 5, 8, 9}

(ii) A U B = {1, 2, 3, 4, 5, 7, 9}

(iii) A U B = {1, 2, 3, 4, 5, 6}

(iv) A U B = {1, 2, 3, 4, 5}

(v) A U B = {a, b, c, d, e, f}

1. Find the intersection of A and B, and respect it by Venn diagram:

(i) A = {a, c, d, e}, B = {b, d, e, f}

(ii) A = {1, 2, 4, 5}, B = {2, 5, 7, 9}

(iii) A = {1, 3, 5, 7}, B = {2, 5, 7, 10, 12}

(iv) A = {1, 2, 3}, B = {5, 4, 7}

(v) A = {a, b, c}, B = {1, 2, 9}

Solution:

(i) A ∩ B = {d, e}

(ii) A ∩ B = {2, 5}

(iii) A ∩ B = {5, 7}

(iv) A ∩ B = { }

1. Find A B and A B when:

(i) A is the set of all prime numbers and B is the set of all composite natural numbers:

(ii) A is the set of all positive real numbers and B is the set of all negative real numbers:

(iii) A = N and B = Z:

(iv) A = {x /x Z and x is divisible by 6} and

B = {x / x Z and x is divisible by 15}

(v) A is the set of all points in the plane with integer coordinate and B is the set of all points with rational coordinates

Solution:

(i) A = {2, 3, 5, 7….}

B = {1, 4, 6….}

A U B = {1, 2, 3, 4} = N

A ∩ B = { }

(ii) A = R+

B = R+

A U B = R – {10}

i.e. A U B ={set of non zero real numbers}

A U B = { }

(iii) A = N B = N

A U B = Z

A ∩ B = N

(iv) A U B = {x / x € Z and x is divisible by 6 and 15} and

A ∩ B = {x / x € Z and x is divisible by 30}

[LCM of 6 and 15 = 30]

(v) A U B = the set of all points with rational co-ordinates = B.

A ∩ B = the set of all points with rational co-ordinates = A.

1. Give examples to show that

(i) A U A = A and A A = A

(ii) If A B, then A U B = B and A B =A. can you prove these statements formally?

Solution:

(i) If A = {2 4 6 8}

Then A U A = {2, 4, 6, 8……} = A

A ∩ A = {2, 4, 6, 8…….} = A

Hence A U A = A and A ∩ A = A

(ii) A = {1, 3, 5, 7, 9……}

B = {1, 2, 3, 4, 5……}

We see that A ⸦ B

A U B = {1 2 3 4…..} = B

A ∩ B = B

A ∩ B = {1, 3, 5……} = A

A ∩ B = A

1. What is A U Φ and A ∩ Φ for a set A?

Solution:

AUΦ = A ;  A ∩Φ = Φ

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