math 9th 3.1.pptx pctb pakistan sylabuss

9th class pctb book best notes prepared by imran ali m.phil computer, msc maths

1. Answers: i. {x | x ∈ n², n ∈ ℕ ∧ 1 ≤ n ≤ 22} ii. {x | x ∈ 2ⁿ, n ∈ ℕ ∧ 1≤ n ≤ 7} iii. {x | x ∈ ℤ ∧ 0 ≤ x ≤ 1000} iv. {x | x ∈ 6n, n ∈ ℕ ∧ 1≤ n ≤ 20} v. {x | x ∈ 2n+100, n ∈ W ∧ 0 ≤ n ≤ 150} or v. {x | x ∈ E+, ∧ 100 ≤ x ≤ 400} vi. {x | x ∈ 3ⁿ, n ∈ W} vii. {x | x is divisor of 100} viii. {x | x ∈ 5n, n ∈ ℕ, ∧ 1 ≤ n ≤ 20} ix. {x | x ∈ ℤ, -100 < x < 1000}  

2. Answers :

3. Answers: i) {a , b},{c} ii ) {0} , {1} iii ) { 1, 2, 3},{1} E iv ) N, E v ) Z , N vi ) Q , Q ’ vii ) {x | x ∈ Q, 0 < x ≤1} , {x | x ∈ Q, 1 ≤ x ≤ 2}

4. Answer : yes, {} or ∅ Answer : {a, b}: This is a simple set containing two elements: 'a' and 'b'. {{a, b}}: This is a set containing only one element i)Number of power set = = 1 ii)Number of power set = = 4 iii)Number of power set = = 128   iv)Number of power set = 256 v)Number of power set = = 4 vi)Number of power set = = 8  

5. i ) Power Set : {{}, {9}, {11}, {9, 11}} ii )Power Set: {{}, {+}, {-}, {×}, {÷}, {+, -}, {+, ×}, {+, ÷}, {-, ×}, {-, ÷}, {×, ÷}, {+, -, ×}, {+, -, ÷}, {-, ×, ÷}, {+, ×, ÷}, {+, -, ×, ÷}} iii ) Power Set : { φ , { φ }} iv ) Power Set : {{}, {a},{a, b },{a, {b, c}}}