Notes on Set Operations | Grade 7 > Compulsory Maths > Sets | KULLABS.COM

Set Operations

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There are four fundamental or basic set operations. They are given below:

  • Union of sets
  • Intersection of sets
  • Difference of sets
  • Complement of a set

  1. Union of sets

    The union of any two sets A and B is the set of all elements belonging either to A or to B or to both. It is denoted by (AUB) which is read as 'A union B'. The symbol 'U' (cup) is used to denote the union of sets. For example,
    A = {a, b, c, d, e}
    B = {a, e, i, o, u}
    AUB = {a, b, c, d, e} U {a, e, i, o, u}
    = {a, b, c, d, e, i, o, u}

  2. Intersection of sets

    The intersection of any two sets A and B is the set of all elements of both A and B. It is the set of all elements of both A and B. It is denoted by (A∩B) which is read as 'An intersection B'. The symbol '∩' (cup) is used to denote the intersection of sets. For examples:
    A = {a, b, c, d, e}
    B = {a, e, i, o, u}
    A∩B = {a, b, c, e, d}∩ {a, e, i, o, u}
    = (a, e}

  3. Different of sets









    Two sets A and B is called different if the sets. of all the elements that belong to A does not belong to B. It can be written as(A - B). For examples:
    A = (a, b, c, d, e}
    B = {a, e, i,o, u}
    A - B = {a, b, c, d, e} - {a, e, i, o, u}
    = {b, c, d}
    B - A = {a, b, c, d, e} - {a, e, i, o, u}
    = {i, o, u}

  4. Complement of a sets
    If 'U' be the universal set and A is its subset, then the complement to A is the set of all elements that belong to 'U' but not to A. It can be written as A' or \(\overline{A}\) or Ac. For example:
    U = {a, b, c, d, e, f, g, h}
    A = {a, b, c, d, e}
    \(\overline{A}\) = U - A
    = {a, b, c, d, e, f, g, h} - {a, b, c, d, e}
    = {f, g, h}



  1. There are four fundamental or basic set operations. They are Union of sets, Intersection of sets, Difference of sets, and Complement of a set.
  2. The intersection of any two sets A and B is the set of all elements of both A and B. 
  3. Two sets A and B is called different if the sets. of all the elements that belong to A does not belong to B. It can be written as(A - B). 
  4. If 'U' be the universal set and A is its subset, then the complement to A is the set of all elements that belong to 'U' but not to A.
  5. The union of any two sets A and B is the set of all elements belonging either to A or to B or to both. It is denoted by (AUB) 

 

.

Very Short Questions

Solution:

Here, 


P = {a, e, i, o, u}
Q = {a, b, c, d, e}
Now,
P∪Q = {a, b, c, d, e, i, o, u}
The shahded region represents the elements of P∪Q.

P∩Q = {a, e}
The shahded region represents the elements of P∩Q

P - Q = {i, o, u}
The shahded region represents the elements of P - Q

Q - P = {b, c, d}
The shahded region represents the Q - P

Solution:

Here,
A = {2, 4, 6, 8, 10, 12}
B = {1, 2, 3, 4, 5, 6}
C = {2, 3, 5, 7, 11}
Now, 
B∪C = {1, 2, 3, 4, 5, 6, 7, 11}
∴ A∪(B∪C) = {1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12}
Again,
A∪B = {1, 2, 3, 4, 5, 6, 8, 10, 12}
∴ (A∪B)∪C = {1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12}
∴ A∪(B∪C) = (A∪B)∪C proved.

Solution:

Here, 
\(\overline{A∪B}\) = {4, 6, 7}
\(\overline{A}\) ∩ \(\overline{B}\) = {4, 5, 6, 7, 8, 9} ∩ {1, 3, 4, 6, 7} 
\(\overline{A}\) ∩ \(\overline{B}\) = {4, 6, 7}

Again,
\(\overline{A∩B}\) = {1, 3, 4, 5, 6, 7, 8, 9}
\(\overline{A}\) ∪ \(\overline{B}\) = {4, 5, 6, 7, 8, 9} ∪ {1, 3, 4, 6, 7}
\(\overline{A}\) ∪ \(\overline{B}\) = {1, 3, 4, 5, 6, 7, 8, 9}

0%
  • There are ______ fundamental or basic set operations.

    five
    six
    two
    four
  • Union of set is denoted by _______.

    Ü

    µ

  • Intersection of a set is denoted by ______.


    η
    Π
    Ω
  • If P = {a, e, i, o, u} and Q = {a, b, c,d, e} find P - Q.

    P - Q = {a,b, c, d, e, i, o, u}
    P - Q = {b, c, d}
    P - Q = {i, o, u}
    P - Q = {a, e}
  • If A = {2, 4, 6, 8, 10} and B = {1, 2, 3, 4, 5, 6, 7} find A∩B.

    A∩B = {2, 4, 6}
    A∩B = {1, 2, 4, 6, 8}
    A∩B = {1, 2, 3, ,5, 7}
    A∩B = {1, 3, 5, 7}
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