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
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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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Answer is in attechment.
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