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If A={x:x^(2)-2x+2gt0}andB={x:x^(2)-4x+3...

If `A={x:x^(2)-2x+2gt0}andB={x:x^(2)-4x+3le0}`
A - B equals

A

`(-oo,oo)`

B

(1,3)

C

`(3,oo)`

D

`(-oo,1)uu(3,oo)`

Text Solution

Verified by Experts

The correct Answer is:
D
`A={x:x^(2)-2x+2gt0}={x:(x-1)^(2)+1gt0}=(-oo,oo)`
`B={x:x^(2)-4x+3le0}={x:(x-1)(x-3)le0}`
`={x:1lexle3}=[1,3]`
`A-B=(-oo,oo)-[1,3]=(-oo,1)uu(3,oo)`
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