please show the proof of (f), (h), (i) TheoremLet a, b, c ER.(a) If a < b and b< c, then a < c.(Tra(b) If a < b, then a +c 0.(TB1>0(g) If a > b and c> d, then a + c > b + d.Th) If a > b > 0 and c> d> 0, then ac > bd.i) If a> b> 0, then b-1> a-1.

For (f) ,We use a theorem that "if n∈ℤ and n≠0 then n2>0.

Answered: (B1>0 (g) If a > b and c> d, then a + c…

(B1>0 (g) If a > b and c> d, then a + c > b + d. h) If a > b> 0 and c > d > 0, then ac > bd. i) If a > b> 0, then b-1 > a-1.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 56E

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Question

please show the proof of (f), (h), (i)

Theorem
Let a, b, c ER.
(a) If a < b and b< c, then a < c.
(Tra
(b) If a < b, then a +c <b+c.
(Addition F
(c) If a < b and 0 < c, then ac < bc.
(Multiplication
(d) If a < b and c < 0, then bc < ac.
(Multiplication
(e) If a 0, then a2 = a· a > 0.
(TB1>0
(g) If a > b and c> d, then a + c > b + d.
Th) If a > b > 0 and c> d> 0, then ac > bd.
i) If a> b> 0, then b-1> a-1.

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