Introduction to Discrete Mathematics Set Theory
In discrete mathematics, the set theory are the branch of mathematics that learned about the sets, which are the collections of objects. Even though any type of objects can be collected into a set, set theory is applied most often to objects that are related to mathematics. Now we will see the examples of discrete mathematics set theory.(Source: Wikipedia).
Venn Diagrams for Discrete Mathematics Set Theory
A∪B
The A∪B means all elements of A and B sets. Venn diagram for A∪B is as follows,
A∩B
The B∩C is a common element of the sets. Venn diagram representation is given below,
A –B
The A-B is the values of A which is not in B set. Venn diagram representation is given below,
Examples for Discrete Mathematics Set Theory
1)Proof the A∪(B∩C)=(A∪B) ∩(A∪C) for the following sets.
A={3,6,9,15,17} B={12,13,14,19,21} C={3,7,8,10,12}
Solution
The given sets are A={3,6,9,15,17} B={12,13,14,19,21} C={3,7,8,10,12}
Given condition is A∪(B∩C)=(A∪B) ∩(A∪C)
Take the left side condition.
A∪(B∩C)
B∩C
Take the common values of the sets B and C.
B∩C={12}
A∪(B∩C)
Now joining the A set values.
A∪(B∩C)={ 3,6,9,12,15,17} ----(1)
Take right side condition.
(A∪B) ∩(A∪C)
A∪B={3,6,9,12,13,14,15,17,19,21}
A∪C={3,6,7,8,9,10,12,15,17}
(A∪B) ∩(A∪C)={3,6,9,12,15,17} ----(2)
Therefore A∪(B∩C)=(A∪B) ∩(A∪C).
2) Proof the A∪(B∩C)=(A∪B) ∩(A∪C) condition for the sets A={3,6,7,9,10} B={1,4,5,7,8} C={3,6,8,9,10}. Please express your views of this topic board of secondary education ap by commenting on blog.
Solution
The given sets are A={3,6,7,9,10} B={1,4,5,7,8} C={3,6,8,9,10}
Take left hand side condition.
A∩(B∪C)
B∪C={1,3,4,5,6,7,8,9,10}
A∩(B∪C)={3,6,7,9,10} ----(1)
Now take the right hand side condition.
(A∩B) ∪ (A∩C)
A∩B={7}
A∩C={3,6,9,10}
(A∩B) ∪ (A∩C)={3,6,7,9,10} ----(2)
Therefore A∩(B∪C)=(A∩B) ∪ (A∩C).
3)A={1,4,7,9,10} B={3,6,9,12,14} and C={2,7,8,12,13}. Find the i)A-(B∪C) ii)B-(A∪C).
Solution
The given sets are A={1,4,7,9,10} B={3,6,9,12,14} and C={2,7,8,12,13}.
i) A-(B∪C)
B∪C={2,3,6,7,8,9,12,13,14}
A-( B∪C) condition is a difference of set. It means we select the values from the A set. But that value is not present in the B∪C set.
So A- B∪C={1,4,10}
ii)B-(A∪C)
A∪C={1,2,4,7,8,9,10,12,13}
B-(A∪C)={3,6,14}
These are the examples of discrete mathematics set theory.
In discrete mathematics, the set theory are the branch of mathematics that learned about the sets, which are the collections of objects. Even though any type of objects can be collected into a set, set theory is applied most often to objects that are related to mathematics. Now we will see the examples of discrete mathematics set theory.(Source: Wikipedia).
Venn Diagrams for Discrete Mathematics Set Theory
A∪B
The A∪B means all elements of A and B sets. Venn diagram for A∪B is as follows,
A∩B
The B∩C is a common element of the sets. Venn diagram representation is given below,
A –B
The A-B is the values of A which is not in B set. Venn diagram representation is given below,
Examples for Discrete Mathematics Set Theory
1)Proof the A∪(B∩C)=(A∪B) ∩(A∪C) for the following sets.
A={3,6,9,15,17} B={12,13,14,19,21} C={3,7,8,10,12}
Solution
The given sets are A={3,6,9,15,17} B={12,13,14,19,21} C={3,7,8,10,12}
Given condition is A∪(B∩C)=(A∪B) ∩(A∪C)
Take the left side condition.
A∪(B∩C)
B∩C
Take the common values of the sets B and C.
B∩C={12}
A∪(B∩C)
Now joining the A set values.
A∪(B∩C)={ 3,6,9,12,15,17} ----(1)
Take right side condition.
(A∪B) ∩(A∪C)
A∪B={3,6,9,12,13,14,15,17,19,21}
A∪C={3,6,7,8,9,10,12,15,17}
(A∪B) ∩(A∪C)={3,6,9,12,15,17} ----(2)
Therefore A∪(B∩C)=(A∪B) ∩(A∪C).
2) Proof the A∪(B∩C)=(A∪B) ∩(A∪C) condition for the sets A={3,6,7,9,10} B={1,4,5,7,8} C={3,6,8,9,10}. Please express your views of this topic board of secondary education ap by commenting on blog.
Solution
The given sets are A={3,6,7,9,10} B={1,4,5,7,8} C={3,6,8,9,10}
Take left hand side condition.
A∩(B∪C)
B∪C={1,3,4,5,6,7,8,9,10}
A∩(B∪C)={3,6,7,9,10} ----(1)
Now take the right hand side condition.
(A∩B) ∪ (A∩C)
A∩B={7}
A∩C={3,6,9,10}
(A∩B) ∪ (A∩C)={3,6,7,9,10} ----(2)
Therefore A∩(B∪C)=(A∩B) ∪ (A∩C).
3)A={1,4,7,9,10} B={3,6,9,12,14} and C={2,7,8,12,13}. Find the i)A-(B∪C) ii)B-(A∪C).
Solution
The given sets are A={1,4,7,9,10} B={3,6,9,12,14} and C={2,7,8,12,13}.
i) A-(B∪C)
B∪C={2,3,6,7,8,9,12,13,14}
A-( B∪C) condition is a difference of set. It means we select the values from the A set. But that value is not present in the B∪C set.
So A- B∪C={1,4,10}
ii)B-(A∪C)
A∪C={1,2,4,7,8,9,10,12,13}
B-(A∪C)={3,6,14}
These are the examples of discrete mathematics set theory.
