Question

let A= { 1, 2 , 3, 4 } and B = { 2,3,4,5,6 }
then A Δ B equals what

Answer 1

Here, A = {1, 2, 3, 4} and B = {2, 3, 4, 5, 6}.

The symmetric difference of A and B (A Δ B) contains the elements which are other than A ∩ B in both sets.

Here, A ∩ B = {1, 2, 3, 4} ∩ {2, 3, 4, 5, 6} = {2, 3, 4}

Now we have to take  A \ (A ∩ B)  and  B \ (A ∩ B).

→  A \ (A ∩ B) = {1, 2, 3, 4} \ {2, 3, 4} = {1}

→  B \ (A ∩ B) = {2, 3, 4, 5, 6} \ {2, 3, 4} = {5, 6}

The union of these two is the answer.

∴ A Δ B = (A \ (A ∩ B) ∪ {B \ (A ∩ B)} = {1} ∪ {5, 6} = {1, 5, 6}.

Thus, A Δ B = {1, 5, 6}

Or we can use this formula:

    A Δ B = (A \ B) ∪ (B \ A)

⇒  A Δ B = ({1, 2, 3, 4} \ {2, 3, 4, 5, 6}) ∪ ({2, 3, 4, 5, 6} \ {1, 2, 3, 4})

⇒  A Δ B = {1} ∪ {5, 6}

⇒  A Δ B = {1, 5, 6}