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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}`
`AnnB` equals

A

`[1,oo]`

B

[1,3]

C

`(-oo,3]`

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
`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]`
`AnnB=(-oo,oo)nn[1,3]=[1,3]`
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