Question

Find \[A\Delta B\] and draw Venn diagram when: \[A = \left\{ {1,4,7,8} \right\}\] and \[B = \left\{ {4,8,6,9} \right\}\].

Answer 1

Hint:
Here we will firstly find the value of the whole set of numbers i.e. union of both the set. Then we will find the value of only the common number between \[A\] and \[B\] i.e. the intersection of both the sets. Then we will subtract intersection from the union of the set to get the value of \[A\Delta B\]. Then we will draw the Venn diagram for it.

Complete step by step solution:
Given sets are \[A = \left\{ {1,4,7,8} \right\}\] and \[B = \left\{ {4,8,6,9} \right\}\].
Firstly we will find the value of whole set of number i.e. \[A \cup B\]. Therefore, we get
\[A \cup B = \left\{ {1,4,7,8} \right\} \cup \left\{ {4,8,6,9} \right\} = \left\{ {1,4,7,6,8,9} \right\}\]
Then we will find the value of only common number between \[A\] and \[B\] i.e. \[A \cap B\]. Therefore, we get
\[A \cap B = \left\{ {1,4,7,8} \right\} \cap \left\{ {4,8,6,9} \right\} = \left\{ {4,8} \right\}\]
Now we will find the value of \[A\Delta B\] which is the set of numbers which occur only in one particular set. Therefore, by subtracting \[A \cap B\] from \[A \cup B\] to get the value of \[A\Delta B\], we get
\[A\Delta B = A \cup B - A \cap B = \left\{ {1,4,7,6,8,9} \right\} - \left\{ {4,8} \right\} = \left\{ {1,7,6,9} \right\}\]
Hence the value of \[A\Delta B\] is \[\left\{ {1,7,6,9} \right\}\]
Now we will draw the Venn diagram of the given sets. Therefore, we get

Note:
Venn diagram is the diagram which shows all the possible relations between different sets of data. Venn diagrams are also termed as the primary diagram or logic diagram or set diagram. The area intersected by two circles is the area for the elements which are common in those two groups or sets. We should draw the Venn diagram carefully and keep in mind that in the common region the data may not repeat. The set which includes all the elements from every set of data is denoted as \[A \cup B\]. The set which includes only common terms between the given sets is generally denoted as \[A \cap B\]. Venn diagrams are generally used for showing some relation between different things or different groups of things or items.