**Advanced Mathematics Class X Exercise 1.1**

**Advanced Maths Ex 1.1 **

**Exercise 1.1 Advanced Maths Class 10** : This page includes the full solutions of **Class 10 Advanced Maths 1.1** exercise. All the questions are prepared by a experienced staff of teachers. Read Now!

ADVANCED MATHEMATICS

**Exercise 1.1**

1. For the sets A = {x : x ∈ N and x ≤ 10 } and Ф . Find the following-
Solution: Here, A = {x : x ∈ N and x ≤ 10 } = {1,2,3,….,10} and Ф is the empty set (means no any elements). .’. (a) n(A) = 10 and n(Ф) = 0 (b) n(A ∪ Ф) = n(A) = 10 and n(A n Ф) = n(Ф) = 0 |

2. Let A and B be two sets and U be their universal set. If n(U) = 120 , n(A) = 42 , n(B) = 50 and n(A n B) = 21 , then find,
Solutions: Given, n(U) = 120 , n(A) = 42 , n(B) = 50 and n(A n B) = 21 (i) n(A ∪ B) = n(A) + n(B) – n(A n B) = 42 + 50 – 21 = 71 n(A – B) = n(A) – n(A n B) = 42 – 21 = 21 n(B – A) = n(B) – n(A n B) = 50 -21 = 29 (ii) n(B’) = n(U) – n(B) = 120 – 50 = 70 n(A’) = n(U) – n(A) = 120 – 42 = 78 n(A ∪ B)’ = n(U) – n(A U B) = 120 – 71 = 49 (iii) n(P U Q) = n{(A – B) U (A n B)} =n{(A n B’) U (A n B)} = n{A U (B’ n B)} =n(A U Ф) = n(A) = 42 And, n(P n Q) = n{(A – B) n (A n B)} = n{(A n B’) n (A n B)} = n{A n (B’ n B)} = n(A n Ф) = n(Ф) = 0 (iii) n{U – (A U B)} = n(U) – n{U n (A U B)} =n(U) – n(A U B) = 120 – 71 = 49 |

3. If n(A n B) = 36, n(A – B) = 25, n(B – A) = 20 then find n(A U B), n(A) and n(B).Solutions: Given, n(A n B) = 36, n(A – B) = 25, n(B – A) = 20 .’. n(A U B) = n(A – B) + n(B – A) + n(A n B) = 25 + 20 + 36 = 81` Secondly, n(A) = n(A – B) + n(A n B) = 25 + 36 = 61 Lastly, n(B) = (B – A) + n(A n B) = 20 + 36 = 56 |

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