Question

Let A= set of all rational numbers and B={ x:x square-4x+2=0}. Then find A-B, B-A and A union B. Explain in detail.​

Answer 1

Answer:

Step-by-step explanation:

Given:  A= set of all rational numbers and B={ x:x square-4x+2=0}.

To find: A-B, B-A and A union B.

Solution:

        · The set B is x: x square-4x+2=0

        · Now we need to find the value of x, by finding roots.

                   x^2 - 4x + 2 = 0

                   x = 4 ± √16 - 8 / 2

                   x = 4 ± √8 / 2

                   x = 4 ± 2√2 / 2

                   x = 2 ± √2

          · So the value of x is 2 ± √2

                   A-B = { x: x belongs to Z }

                   B- A = { 2 ± √2 }

                   A ∪ B = { all rational numbers +  2 ± √2 }

Answer:

              So A-B = { x: x belongs to Z } , B- A = { 2 ± √2 }, A ∪ B = { all rational numbers +  2 ± √2 }

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