2022TrialShort answer

Q14 (a)

2 marks

Question

If $x\le1$ and $y\ge1$ , show that $x+y\ge1+xy$ .

Try the question before revealing the answer.

Solution

$x\le 1$

$x-1\le 0$ $I$

$y\ge 1$

$y-1\ge 0$ $II$

$(y-1)(x-1)\le 0$

From I and II,

$xy-x-y+1\le 0$
$xy+1\le x+y$
$x+y\ge xy+1$

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Syllabus alignment

Proof

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

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