Let P be the statement ' k >= 2 ' and Q be the statement ' x 2 - 2x + k >= 1 for every real x '. Which of the following is correct? (Here k is a real number.)

P is both a necessary and a sufficient condition for Q

P is a necessary but not a sufficient condition for Q

P is neither a necessary nor a sufficient condition for Q

P is a sufficient but not a necessary condition for Q

Let $P$ be the statement ' $k \geq 2$ ' and $Q$ be the statement ' $x^{2} - 2 x + k \geq 1$ for every real $x$ '. Which of the following is correct? (Here $k$ is a real number.)

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