tmua.fyi Mock Paper 2 · Question 18

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tmua.fyi Mock Paper 2 · Q18

Paper 2Logic & proofFunctions & graphs

$f$ is a continuous function and $a<b$ . Consider statement P: ‘ $f(a)$ and $f(b)$ have opposite signs’, and statement Q: ‘ $f$ has a root in the open interval $(a,b)$ ’. Then P is:

Anecessary but not sufficient for Q.

Bsufficient but not necessary for Q.

Cboth necessary and sufficient for Q.

Dneither necessary nor sufficient for Q.

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