TMUA Specimen Paper 2 Q17 — Worked Solution

P2·Logic & Quantifiers, Number Theory & Divisibility·6.5Specimen · P2 · Q17

quantifier-negationnested-quantifiersset-membership

Let

S

be a set of positive integers, for example

S

could consist of

3

4

, and

8

.A positive integer

n

is called an

S

-number if and only if for every factor

m

n

with

m > 1

, the number

m

is a multiple of some number in

S

.So in the above example,

9

is an

S

-number; this is because the factors of

9

greater than

1

are

3

and

9

, and each of these is a multiple of

3

.Positive integer

n

is therefore not an

S

-number if and only if

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