Plus One Math's Solution Ex 1.4 Chapter 1 Sets

 

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Board SCERT, Kerala
Text Book NCERT Based
Class Plus One 
Subject Math's Textbook Solution
Chapter Chapter 1
Exercise Ex 1.4
Chapter Name Sets
Category Plus One Kerala


Kerala Syllabus Plus One Math's Textbook Solution Chapter  1 Sets Exercises 1.4


Chapter  1  Sets Textbook Solution



Kerala plus One maths NCERT textbooks, we provide complete solutions for the exercise and answers provided at the end of each chapter. We also cover the entire syllabus given by the Board of secondary education, Kerala state.

Chapter  1  Sets Exercise   1.4

    If X = {abcd} and Y = {fbd, g}, find

    (i) X – Y

    (ii) Y – X

    (iii) X ∩ Y

    (i)X-Y={a,c}

    Elements present in X but not in Y

    (ii)Y-X={f,g}

    Elements present in Y but not in X

    (iii)X∩Y={b,d}

    elements common to X  and Y

    If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?

    Q is the subset of R.

    set of real numbers other than rational numbers are irrational numbers.

    R-Q=irrational numbers

    State whether each of the following statement is true or false. Justify your answer.

    (i) {2, 3, 4, 5} and {3, 6} are disjoint sets.

    (ii) {aeiou } and {abcd} are disjoint sets.

    (iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.

    (iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.

    (i) False

    As 3 ∈ {2, 3, 4, 5}, 3 ∈ {3, 6}

    ⇒ {2, 3, 4, 5} ∩ {3, 6} = {3}

    (ii) False

    As a ∈ {aeiou}, a ∈ {abcd}

    ⇒ {aeiou } ∩ {abcd} = {a}

    (iii) True

    As {2, 6, 10, 14} ∩ {3, 7, 11, 15} = Φ

    (iv) True

    As {2, 6, 10} ∩ {3, 7, 11} = Φ

    Find the union of each of the following pairs of sets:

    (i) X = {1, 3, 5} Y = {1, 2, 3}

    (ii) A = {aeiou} B = {abc}

    (iii) A = {xx is a natural number and multiple of 3}

    B = {xx is a natural number less than 6}

    (iv) A = {xx is a natural number and 1 < x ≤ 6}

    B = {xx is a natural number and 6 < x < 10}

    (v) A = {1, 2, 3}, B = Φ

    (i) X = {1, 3, 5} Y = {1, 2, 3}

    X∪ Y= {1, 2, 3, 5}

    (ii) A = {aeiou} B = {abc}

    A∪ B = {abceiou}

    (iii) A = {xx is a natural number and multiple of 3} = {3, 6, 9 …}

    As B = {xx is a natural number less than 6} = {1, 2, 3, 4, 5, 6}

    A ∪ B = {1, 2, 4, 5, 3, 6, 9, 12 …}

    ∴ A ∪ B = {xx = 1, 2, 4, 5 or a multiple of 3}

    (iv) A = {xx is a natural number and 1 x ≤ 6} = {2, 3, 4, 5, 6}

    B = {xx is a natural number and 6 x

    A∪ B = {2, 3, 4, 5, 6, 7, 8, 9}

    ∴ A∪ B = {x: x ∈ N and 1 x

    (v) A = {1, 2, 3}, B = Φ

    A∪ B = {1, 2, 3}

    Let A = {ab}, B = {abc}. Is A ⊂ B? What is A ∪ B?

    Here, A = {ab} and B = {abc}

    Yes, A ⊂ B.

    A∪ B = {abc} = B

    If A and B are two sets such that A ⊂ B, then what is A ∪ B?

    If A and B are two sets such that A ⊂ B, then A ∪ B = B.

    If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

    (i) A ∪ B

    (ii) A ∪ C

    (iii) B ∪ C

    (iv) B ∪ D

    (v) A ∪ B ∪ C

    (vi) A ∪ B ∪ D

    (vii) B ∪ C ∪ D

    1.{1,2,3,4,5,6}

    2.{1,2,3,4,5,6,7,8}

    3.{3,4,5,6,7,8}

    4.{3,4,5,6,7,8,9,10}

    5.{1,2,3,4,5,6,7,8}

    6.{1,2,3,4,5,6,7,8,9,10}

    7.{3,4,5,6,7,8,9,10}

    Find the intersection of each pair of sets:

    (i) X = {1, 3, 5} Y = {1, 2, 3}

    (ii) A = {aeiou} B = {abc}

    (iii) A = {xx is a natural number and multiple of 3}

    B = {xx is a natural number less than 6}

    (iv) A = {xx is a natural number and 1 x ≤ 6}

    B = {xx is a natural number and 6 x

    (v) A = {1, 2, 3}, B = Φ

    (i) X = {1, 3, 5}, Y = {1, 2, 3}

    X ∩ Y = {1, 3}

    (ii) A = {aeiou}, B = {abc}

    A ∩ B = {a}

    (iii) A = {xx is a natural number and multiple of 3} = (3, 6, 9 …}

    B = {xx is a natural number less than 6} = {1, 2, 3, 4, 5}

    ∴ A ∩ B = {3}

    (iv) A = {xx is a natural number and 1 < x ≤ 6} = {2, 3, 4, 5, 6}

    B = {xx is a natural number and 6 < x < 10} = {7, 8, 9}

    A ∩ B = Φ

    (v) A = {1, 2, 3}, B = Φ

    A ∩ B = Φ

    If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find

    (i) A ∩ B

    (ii) B ∩ C

    (iii) A ∩ C ∩ D

    (iv) A ∩ C

    (v) B ∩ D

    (vi) A ∩ (B ∪ C)

    (vii) A ∩ D

    (viii) A ∩ (B ∪ D)

    (ix) (A ∩ B) ∩ (B ∪ C)

    (x) (A ∪ D) ∩ (B ∪ C)

    (i) A ∩ B = {7, 9, 11}

    (ii) B ∩ C = {11, 13}

    (iii) A ∩ C ∩ D = { A ∩ C} ∩ D = {11} ∩ {15, 17} = Φ

    (iv) A ∩ C = {11}

    (v) B ∩ D = Φ

    (vi) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

    = {7, 9, 11} ∪ {11} = {7, 9, 11}

    (vii) A ∩ D = Φ

    (viii) A ∩ (B ∪ D) = (A ∩ B) ∪ (A ∩ D)

    = {7, 9, 11} ∪Φ = {7, 9, 11}

    (ix) (A ∩ B) ∩ (B ∪ C) = {7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11}

    (x) (A ∪ D) ∩ (B ∪ C) = {3, 5, 7, 9, 11, 15, 17) ∩ {7, 9, 11, 13, 15}

    = {7, 9, 11, 15}

    If A = {x: x is a natural number}, B ={x: x is an even natural number}

    C = {x: x is an odd natural number} and D = {x: x is a prime number}, find

    (i) A ∩ B

    (ii) A ∩ C

    (iii) A ∩ D

    (iv) B ∩ C

    (v) B ∩ D

    (vi) C ∩ D

    A = {x: x is a natural number} = {1, 2, 3, 4, 5 …}

    B ={x: x is an even natural number} = {2, 4, 6, 8 …}

    C = {x: x is an odd natural number} = {1, 3, 5, 7, 9 …}

    D = {x: x is a prime number} = {2, 3, 5, 7 …}

    (i) A ∩B = {x: x is a even natural number} = B

    (ii) A ∩ C = {x: x is an odd natural number} = C

    (iii) A ∩ D = {x: x is a prime number} = D

    (iv) B ∩ C = Φ

    (v) B ∩ D = {2}

    (vi) C ∩ D = {x: x is odd prime number}

    Which of the following pairs of sets are disjoint

    (i) {1, 2, 3, 4} and {x: x is a natural number and 4 ≤ x ≤ 6}

    (ii) {aeiou}and {cdef}

    (iii) {x: x is an even integer} and {x: x is an odd integer}

    (i) {1, 2, 3, 4}

    {xx is a natural number and 4 ≤ x ≤ 6} = {4, 5, 6}

    Now, {1, 2, 3, 4} ∩ {4, 5, 6} = {4}

    Therefore, this pair of sets is not disjoint.

    (ii) {aeiou} ∩ (cdef} = {e}

    Therefore, {aeiou} and (cdef} are not disjoint.

    (iii) {xx is an even integer} ∩ {xx is an odd integer} = Φ

    Therefore, this pair of sets is disjoint.

    If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20},

    C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find

    (i) A – B

    (ii) A – C

    (iii) A – D

    (iv) B – A

    (v) C – A

    (vi) D – A

    (vii) B – C

    (viii) B – D

    (ix) C – B

    (x) D – B

    (xi) C – D

    (xii) D – C

    (i)A-B={3,6,9,15,18,21}  

    Elements present in A,but not in B

    (ii)A-C={3,9,15,18,21}

    Elements present in A but not in C

    (iii)A-D={3,6,9,12,18,21}

    Elements present in A but not in D

    (iv)B-A={4,8,16,20}

    Elements present in B but not in A

    (v)C-A={2,4,8,10,14,16}

    Elements present in C but not in A

    (vi)D-A={5,10,20}

    Elements present in D but not in A

    (vii)B-C={20}

    Elements present in B but not in C

    (viii)B-D={4,8,12,16}

    Elements present in B but not in D

    (ix)C-B={2,6,10,14}

    Elements present in C but not in B

    (x)D-B={5,10,15}

    Elements present in D but not in B

    (xi)C-D={2,4,6,8,12,14,16}

    Elements present in C but not in D

    (xii)D-C={5,15,20}

    Elements present in D but not in C

     

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