Symmetric Difference of Sets||How to prove that: A∆B=(AUB)–(A∩B)

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The symmetric difference of two sets A and B, is the set that contains the elements of A and the elements of B, but not the elements of their intersection.

The notation used to represent this can vary, between any of the following: ⊕ , ⊝ or Δ
#symmetricdifference
#settheory
  1. Precious Ugwueze (Maths Experience)
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Wow this second proff is the best
I don't even need to stress myself to understand

tobechinwanagu
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Let's the set of integers (z) be the universal set and sets, A, B and C be defined as follows
A={2x:x is an integer }
B={x: 0 ≤ x ≤ 9}
C={x:-4 < x≤ 0}
Find
1)B - (A ' n C)
2)C∆B
Solution
U={•••, -3, -2, -1, 0, 1, 2, 3, 4, •••}
Z={x: x is an integer }
A={2x: integral angel of 2}
A={•••, -6, -4, -2, 0, 2, 4, 6•••}
B={x:0 ≤ x ≤9}that is integral values ranging from ”0 to 9"
B={0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
C={x: -4, < x ≤ 0}
C={-3, -2, -1, 0}
Let find A ' first
A ' ={•••, -3, -1, 3, •••}
A ' n C = {-3, -1}
(1) B - (A ' n C ) ={0, 1, 2, 3, 4, 5, 6, 7, 8, 9}=B
C∆B =( C u B)-(C n B)
C u B = {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
C n B = {0}
(2) C∆B= {-3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9}

ernestabuchi
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A symmetric different of B =A unin B -A intersection B endiet endemimeta asredagn

gizachewabebe
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Sir pls I've a question...
The proof is it something we should memorize or just take note of?

rosalynlisa