a-b-c-N-Show-that-ab-lt-c-a-b-c-

Question Number 212741 by mathocean1 last updated on 22/Oct/24

a, b, c \in N^{*}

S h o w t h a t a b < c \Rightarrow a + b ⩽ c

Answered by A5T last updated on 22/Oct/24

W L O G; l e t a ⩽ b

\Rightarrow 2 a = a + a ⩽ a + b ⩽ b + b = 2 b ⩽ a b < c w h e n a ⩾ 2

\Rightarrow a + b < c

w h e n a = 1; a b = b < c \Rightarrow b + 1 ⩽ c \equiv a + b ⩽ c

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