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tmua.me Medium Set A Paper 2 · Q6

Paper 2Logic & proofFunctions & graphs

A function ff is defined for all real numbers. Consider the statement:

For every real x, if x<0 or x>3, then f(x)>1.\text{For every real }x,\text{ if }x<0\text{ or }x>3,\text{ then }f(x)>1.

Which of the following statements is logically equivalent to it? Each option applies to every real xx.

AIf 0≤x≤30\leq x\leq3, then f(x)≤1f(x)\leq1.
BIf f(x)>1f(x)>1, then x<0x<0 or x>3x>3.
CIf f(x)≤1f(x)\leq1, then 0≤x≤30\leq x\leq3.
DIf f(x)<1f(x)<1, then 0<x<30<x<3.
EIf f(x)≤1f(x)\leq1, then x≤0x\leq0 or x≥3x\geq3.

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