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

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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)

.

#### Click on the questions below to reveal the answers

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}

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

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

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

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