Clavis TMUA Set A Paper 2 · Question 14 · ExamDay

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Clavis TMUA Set A Paper 2 · Q14

Paper 2Logic & proofNumber & counting

$n$ is a positive integer.

Consider the statement:

$Q$ : $n$ is a multiple of $6$

and the following three conditions:

I $n$ is a multiple of $2$ and $n$ is a multiple of $3$
II $n$ is a multiple of $12$
III $n$ is a multiple of $2$ or $n$ is a multiple of $3$ (or both)

Which row in the following table is correct?

	Condition I is necessary and sufficient for $Q$	Condition II is necessary and sufficient for $Q$	Condition III is necessary and sufficient for $Q$
A	yes	yes	yes
B	yes	yes	no
C	yes	no	yes
D	yes	no	no
E	no	yes	yes
F	no	yes	no
G	no	no	yes
H	no	no	no

ABCDEFGH

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