2022TrialMultiple choice

Q9

1 mark

Question

Which of the following is the negation of the statement:

“ $\forall p\in P$ , $p$ is of the form $4m+1\Rightarrow p$ can be written as a sum of two squares”?

A. $\forall p\in P$ , $p$ is of the form $4m+1$ and $p$ cannot be written as a sum of two squares.
B. $\exists p\in P$ , $p$ is not of the form $4m+1$ and $p$ can be written as a sum of two squares.
C. $\forall p\in P$ , $p$ is not of the form $4m+1$ or $p$ cannot be written as a sum of two squares.
D. $\exists p\in P$ , $p$ is of the form $4m+1$ and $p$ cannot be written as a sum of two squares.

Try the question before revealing the answer.

Syllabus alignment

Proof

The Nature of ProofUse formal proof language, contradiction, counter-examples and rigorous arguments involving numbers and inequalities.

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