If A = x ∈ R: 0

Question

If A = x ∈ R: 0< x <3 and B = x ∈ R: 1 ≤ x ≤ 5 then A Δ B is (A)  x ∈ R: 0< x < l  (B)  x ∈ R: 3 ≤ x ≤ 5  (C)  x ∈ R: 0 < x < 1 or 3 ≤ x ≤ 5  (D) φ

Tardigrade Admin · Accepted Answer

From the given we have in interval notation

A = (0, 3)

and

B = [1, 5]

Clearly

A - B = (0, 1) = {x \in R : 0 < x < 1}

and

B - A = [3, 5] = {x \in R : 3 \leq x \leq 5}

∴ A Δ B = (A - B) \cup (B - A) = (0, 1) \cup [3, 5]

= {x \in R : 0 < x < 1

or

3 \leq x \leq 5}

Q. If $A = {x \in R : 0 < x < 3}$ and $B = {x \in R : 1 \leq x \leq 5}$ then $A Δ B$ is