What is symmetric difference of A and B?

The symmetric difference of two sets A and B is the set (A – B) ∪ (B – A) and is denoted by A △ B. The shaded part of the given Venn diagram represents A △ B. A △ B is the set of all those elements which belongs either to A or to B but not to both. A △ B is also expressed by (A ∪ B) – (B ∩ A).

How do you calculate symmetric difference on set A and B?

A ∆ B = (A U B) – (A ∩ B) It implies that A ∆ B represents a set that contains the elements from the union of two sets, A and B, minus the intersection between them. Symmetric Difference, in other words, is also called disjunctive union. The symbol ∆ is also a binary operator.

What is symmetric difference between two sets with example?

For an example of the symmetric difference, we will consider the sets A = {1,2,3,4,5} and B = {2,4,6}. The symmetric difference between these sets is {1,3,5,6}.

What is the difference between difference and symmetric difference?

Difference: Elements present on one set, but not on the other. Symmetric Difference: Elements from both sets, that are not present on the other.

What do u mean by symmetric difference?

In mathematics, the symmetric difference of two sets, also known as the disjunctive union, is the set of elements which are in either of the sets, but not in their intersection.

Is symmetric difference transitive?

The Symmetric Property states that for all real numbers x and y , if x=y , then y=x . The Transitive Property states that for all real numbers x ,y, and z, if x=y and y=z , then x=z .

What is symmetric difference in sets Class 11?

In terms of set theory, we can say that the symmetric difference of two sets is the difference of union and intersection of those two sets.

What does a Symetrical mean?

(sĭm′ĭ-trē) An exact matching of form and arrangement of parts on opposite sides of a boundary, such as a plane or line, or around a central point or axis.

How do you prove symmetric difference associative?

The symmetric difference is associative. That is, given sets A, B and C, one has (A∆B)∆C = A∆(B∆C). (A∆B)∆C = (B∆C)∆A = A∆(B∆C), where we have used the commutativity of ∆ to obtain the final equality.