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Step-by-step explanation:
Given :-
A = { x €R , 0< x< 3 }
B = { x€R, 1≤x≤5}
To find:-
Find A ∆ B ?
Solution :-
Method -1:-
Given sets are :
A = { x €R , 0< x< 3 }
=> A = { 1,2}
B = { x€R, 1≤x≤5}
=> B = { 1,2,3,4,5}
We know that
A∆B = (A-B) U (B-A)
A-B ={1,2}-{1,2,3,4,5} = { }
B-A = {1,2,3,4,5}-{1,2} = {3,4,5}
Now
(A-B) U ( B-A)
=> { } U { 3,4,5}
=> { 3,4,5}
Therefore, (A-B) U ( B-A) = { 3,4,5}
Method -2:-
A = { 1,2}
B = {1,2,3,4,5}
We know that
A∆B = (AUB)-(AnB)
AUB={ 1,2} U {1,2,3,4,5} = { 1,2,3,4,5}
AnB = { 1,2} n {1,2,3,4,5} = {1,2}
Now,
(AUB)-(AnB)
=> {1,2,3,4,5} -{1,2}
=> {3,4,5}
Therefore, (A-B) U ( B-A) = { 3,4,5}
Answer:-
A∆B for the given problem is { 3,4,5}
Used formulae:-
- A∆B is the symmetric difference of the two sets A and B
- A∆B = (A-B) U (B-A)
- A∆B = (AUB)-(AnB)
- AUB is the set of all elements in either A or in B or in both.
- AnB is the set of all common elements in both A and B.
- A-B is the set of elements in only A
- B-A is the set of elements in only B
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