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}`
`AuuB` equals

A

`(-oo,1)`

B

`(3,oo)`

C

`(-oo,oo)`

D

(1,3)

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The correct Answer is:

C

`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]`
`AuuB=(-oo,oo)uu[1,3]=(-oo,oo)`

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