Exercise 1.1, Unit-1, SETS, Mathematics 7, Punjab Curriculum and Textbook Board

Exercise 1.1

1. Write the following sets in descriptive form.
(i) A = {a, e, i, o, u)             (ii) B = {3, 6, 9, 12, ...} 

(iii) C = {s, p, r , i, n, g}      (iv) D = {a, b, c, ... ,z} 

(v) E = {6, 7, 8, 9, 10}         (vi) F = {0, ±1, ±2} 

(vii) G = {x | x d N / x < 3} (viii) H = {x | x d N / x > 99}

Solutions:

(i) A = {a, e, i, o, u)
Ans. A = Set of vowels of the English alphabet.

(ii) B = {3, 6, 9, 12, ...}
Ans. B = set of multiples of 3.

(iii) C = {s, p, r , i, n, g}
Ans. C = set of letters of the word "spring"

(iv) D = {a, b, c, ... ,z}
Ans. D =set of all small letters of the English alphabet

(v) E = {6, 7, 8, 9, 10}
Ans. E = set of natural number from 6 to 10

(vi) F = {0, ±1, ±2}
Ans. F = set of integer between -3 and +3

(vii) G = {x | x ∈ N ∧ x < 3}
Ans. G = set of the natural numbers less than 3

(viii) H = {x | x ∈ N ∧ x > 99}
Ans. H = set of natural numbers greater than 99.

Ans. A = Set of vowels of the English alphabet.

(ii) B = {3, 6, 9, 12, ...}
Ans. B = set of multiples of 3.

(iii) C = {s, p, r , i, n, g}
Ans. C = set of letters of the word "spring"

(iv) D = {a, b, c, ... ,z}
Ans. D =set of all small letters of the English alphabet

(v) E = {6, 7, 8, 9, 10}
Ans. E = set of natural number from 6 to 10

(vi) F = {0, ±1, ±2}
Ans. F = set of integer between -3 and +3

(vii) G = {x | x ∈ N ∧ x < 3}
Ans. G = set of the natural numbers less than 3

(viii) H = {x | x ∈ N ∧ x > 99}
Ans. H = set of natural numbers greater than 99.

2. Write the following sets in tabular form.
(i) A = Letters of the word hockey

(ii) B = Two colours in the rainbow 

(iii) C = Numbers less than 18 divisible by 3 

(iv) D = Multiples of 5 less than 30 

(v) E = {x I x d W / x > 5} 

(vi) F = {x I x d Z /  -7 < x < -1}

Solutions:
(i) A = Letters of the word hockey
Ans. A ={h,o,c,k,e,y}

(ii) B = Two colours in the rainbow
Ans. B= {Yellow, red} 

(iii) C = Numbers less than 18 divisible by 3
Ans. C ={3,6,9,12,15}

(iv) D = Multiples of 5 less than 30
Ans. D = {5,10,15,20,25} 

(v) E = {x | x ∈ W ∧ > 5}
Ans. E = {6,7,8,9,...... } 

(vi) F = {x / x d Z / -7 < x < -1}
Ans. F = {-6,-5,-4,-3,-2,-1}

3. Write the following sets into the set builder form. 

(i) A = {1,2,3,4,5} 

(ii) B = {2,3,5,7} 

(iii) N = set of natural numbers 

(iv) W = set of whole number 

(v) Z = set of all integers 

(vi) L = {5, 10, 15,20,...} 

(vii) E = set of even numbers between 1 and 10 

(viii) O = set of odd numbers greater than 15 

(ix) C = set of planets in the solar system 

(x) S = set of colours in the rainbow

Solutions:

(1) A = {1,2,3,4,5}
Ans. A = {x | x ∈ N ∧ x < 6}

(ii) B = {2,3,5,7}
Ans. B = {x | x ∈ P ∧ x < 11}

(iii) N = set of natural numbers
Ans. N = {x | x ∈ N }

(iv) W = set of whole number
Ans. W = {x | x ∈ W }

(v) Z = set of all integers 
Ans. Z= {x | x ∈ Z }

(vi) L = {5, 10, 15,20,...} 
Ans. L = {x | x is a multiple of 5}

(vii) E = set of even numbers between 1 and 10 
Ans. E = {x | x ∈ O ∧ 1 < x < 10}

(viii) O = set of odd numbers greater than 15 
Ans. O = {x | x ∈ E ∧ 1 < x < 10}

(ix) C = set of planets in the solar system
Ans. C = {x | x is a planet in the solar system}

(x) S = set of colours in the rainbow
Ans. S = {x | x is a colour in the rainbow}

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