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Question Number 195291 by Matica last updated on 29/Jul/23

$$itisgivena,b,c\in {\mathbb{N}}^{\ast }andab<c.Provethata+b⩽c.$$

Answered by Frix last updated on 29/Jul/23

$$c=ab+1$$$$a+b⩽ab+1$$$$\mathrm{Let}a<b$$$$b-ab⩽1-a$$$$b(1-a)⩽1-a$$$$\mathrm{This}\mathrm{is}\mathrm{always}\mathrm{true}\mathrm{for}a=1\wedge b\in {\mathbb{N}}^{\ast }$$$$\mathrm{For}a>1:$$$$1-a<0\Rightarrow b(1-a)⩽1-a\iff b⩾1\mathrm{which}\mathrm{is}$$$$\mathrm{true}\mathrm{because}b\in {\mathbb{N}}^{\ast }$$

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