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Statement-1 If A = {x |g(x) = 0} and B =...

Statement-1 If A = {x |g(x) = 0} and B = {x| f(x) = 0}, then `A nn B` be a root of `{f(x)}^(2) + {g(x)}^(2)=0`
Statement-2 `x inAnnBimpliesx inAorx inB`.

A

Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1

C

Statement-1 is true, Statement-2 is false

D

Statement-1 is false, Statement-2 is true

Text Solution

Verified by Experts

The correct Answer is:
C
Let `alphain(AnnB)impliesalphainAandalphainB`
`implies g(alpha)=0`
`andf(alpha)=0`
`implies {f(alpha)}^(2)+{g(alpha)}^(2)=0`
`implies alpha" is a root of "{f(x)}^(2)+{g(x)}^(2)=0`
Hence, Statement-1 is true and Statement-2 is false.
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