examday

Community mocks

Daniel J Smith Custom TMUA alpha · Q18

Logic & proof

Let f(x)f(x), g(x)g(x) and h(x)h(x) be real functions and consider the statement

(∗)(*) If x>0x>0 and f(x)≤0f(x)\leq0 then g(x)≠1g(x)\neq1 or h(x)≥−1h(x)\geq-1.

Which of the following statements is the contrapositive of (∗)(*)?

AIf g(x)=1g(x)=1 and h(x)<−1h(x)<-1 then x≤0x\leq0 or f(x)>0f(x)>0.
BIf g(x)=1g(x)=1 or h(x)<−1h(x)<-1 then x≤0x\leq0 or f(x)>0f(x)>0.
CIf x≤0x\leq0 or f(x)>0f(x)>0 then g(x)=1g(x)=1 and h(x)<−1h(x)<-1.
DIf g(x)≠1g(x)\neq1 or h(x)≥−1h(x)\geq-1 then x>0x>0 and f(x)≤0f(x)\leq0.
EIf x>0x>0 and f(x)≤0f(x)\leq0 then g(x)=1g(x)=1 and h(x)<−1h(x)<-1.

Read the questions freely. Sign in to check your answer, see the worked solution and save your progress.

Sign in to check your answerPractise the whole paper →