TMUA 2022 Paper 2 Q16 — Worked Solution

P2·Inequalities, Logic & Quantifiers·7.0Official · 2022 · Q16

min-maxmust-be-truecounterexample

In this question,

a_{1}, \dots, a_{100}

and

b_{1}, \dots, b_{100}

and

c_{1}, \dots, c_{100}

are three sequences of integers such that

a_{n} \leq b_{n} + c_{n}

for each

n

.Which of the following statements must be true?

(minimum of a_{1}, \dots, a_{100}) \leq (minimum of b_{1}, \dots, b_{100}) + (minimum of c_{1}, \dots, c_{100})

(minimum of a_{1}, \dots, a_{100}) \geq (minimum of b_{1}, \dots, b_{100}) + (minimum of c_{1}, \dots, c_{100})

III

(maximum of a_{1}, \dots, a_{100}) \leq (maximum of b_{1}, \dots, b_{100}) + (maximum of c_{1}, \dots, c_{100})

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