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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 June 9th, 2017, 12:19 AM #1 Senior Member   Joined: Apr 2010 Posts: 451 Thanks: 1 inequality Can somebody give me a complete solution to the following problems: 1) $\displaystyle a\geq b\wedge b\geq c\Longrightarrow a\geq c$ 2) $\displaystyle a\geq b\wedge b\geq a\Longrightarrow a=b$ 3) given a>0 find b>0 such that : $\displaystyle |x-1|  June 9th, 2017, 02:28 AM #2 Global Moderator Joined: Dec 2006 Posts: 18,426 Thanks: 1462 How are you supposed to set out a solution for the first two problems?  June 9th, 2017, 03:03 AM #3 Senior Member Joined: Dec 2015 From: Earth Posts: 192 Thanks: 23 1)$\displaystyle a\geq b \land b\geq c \implies a\geq b \geq c \implies a\geq c$2)$\displaystyle a\geq b \land b \geq a \implies a\geq b \geq a \implies a=b$ June 9th, 2017, 04:50 AM #4 Math Team Joined: Jan 2015 From: Alabama Posts: 2,922 Thanks: 785 What "properties" of "greater than" do you know? For example, are you allowed to use the fact that "greater than" is transitive: that if a> b and b> c then a> c? What do you know? What definition of "$a\ge b$" are you using? June 9th, 2017, 02:20 PM #5 Senior Member Joined: Apr 2010 Posts: 451 Thanks: 1 Quote:  Originally Posted by Country Boy What "properties" of "greater than" do you know? For example, are you allowed to use the fact that "greater than" is transitive: that if a> b and b> c then a> c? What do you know? What definition of "$a\ge b$" are you using? axioms: 1) trichotomy law for ">" 2) a>b and b>c => a>c 3) a>b => a+c>b+c 4) a>b and c>0 => ac>bc Definitions:$\displaystyle a\geq b \Longleftrightarrow a>b \vee a=b\$

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