
Find \[A\Delta B\] and draw Venn diagram when:
\[A = \left\{ {a,b,c,d,e} \right\}\] and \[B = \left\{ {a,c,e,g} \right\}\]
Answer
521.4k+ views
Hint: In this particular question find the elements that are not common to the set A and B because \[A\Delta B\] is a set of all elements which are not in both sets (i.e. uncommon elements).
Complete step-by-step solution:
Now as we know that Venn’s diagram is a diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), and common elements of the set are represented by intersections of the circle or closed curves.
So, now let us first draw the Venn’s diagram for the set A and B.
As we can see from the above Venn’s diagram that the element {b, d, g} does not belong to both the sets or in other words each of the elements of set {b, d, g} either belong to set A or set B.
So, \[A\Delta B = \left\{ {b,d,g} \right\}\]
Because \[A\Delta B\] is the set of all elements that are not present in all sets.
Hence, \[A\Delta B = \left\{ {b,d,g} \right\}\].
Note: Whenever we face such types of questions the key concept recall is that if there are two sets X and Y then \[X\Delta Y\] will be set having elements that are not present in both the sets X and Y. So, we can directly find the value of \[X\Delta Y\] by applying the formula that is \[X\Delta Y = \left( {X \cup Y} \right) - \left( {X \cap Y} \right)\], where \[\left( {X \cup Y} \right)\] will be the set of all elements of set X and Y. While \[\left( {X \cap Y} \right)\] will be the set of common elements of set X and Y. This will be the easiest and efficient way to find the solution to the problem if the Venn’s diagram is not asked to draw.
Complete step-by-step solution:
Now as we know that Venn’s diagram is a diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), and common elements of the set are represented by intersections of the circle or closed curves.
So, now let us first draw the Venn’s diagram for the set A and B.

As we can see from the above Venn’s diagram that the element {b, d, g} does not belong to both the sets or in other words each of the elements of set {b, d, g} either belong to set A or set B.
So, \[A\Delta B = \left\{ {b,d,g} \right\}\]
Because \[A\Delta B\] is the set of all elements that are not present in all sets.
Hence, \[A\Delta B = \left\{ {b,d,g} \right\}\].
Note: Whenever we face such types of questions the key concept recall is that if there are two sets X and Y then \[X\Delta Y\] will be set having elements that are not present in both the sets X and Y. So, we can directly find the value of \[X\Delta Y\] by applying the formula that is \[X\Delta Y = \left( {X \cup Y} \right) - \left( {X \cap Y} \right)\], where \[\left( {X \cup Y} \right)\] will be the set of all elements of set X and Y. While \[\left( {X \cap Y} \right)\] will be the set of common elements of set X and Y. This will be the easiest and efficient way to find the solution to the problem if the Venn’s diagram is not asked to draw.
Recently Updated Pages
Power set of empty set has exactly subset class 11 maths CBSE

While covering a distance of 30km Ajeet takes 2 ho-class-11-maths-CBSE

Sanjeevani booti brought about by Lord Hanuman to cure class 11 biology CBSE

A police jeep on patrol duty on a national highway class 11 physics CBSE

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Trending doubts
1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE

Whales are warmblooded animals which live in cold seas class 11 biology CBSE

What is Environment class 11 chemistry CBSE
