Proof of addition and subtraction rules for systems of inequalities. a < b and c

minwaardekn

minwaardekn

Answered question

2022-06-12

Proof of addition and subtraction rules for systems of inequalities.
a < b and c < d
Then a + c < b + d is a valid move, but subtraction isn't. And similarly for a system such as e > f and g < h then e g > f h is valid and so is g e < h f, but addition isn't valid.

Answer & Explanation

gaiageoucm5p

gaiageoucm5p

Beginner2022-06-13Added 20 answers

Given a < b and c < d then a + c < b + c < b + d
Given e > f and g < h then e g > f g > f h
Damon Stokes

Damon Stokes

Beginner2022-06-14Added 6 answers

a < b x > 0 , a + x = b.
Similarly c < d y > 0 , c + y = d.
Thus we have a + c + ( x + y ) = b + d a + c < b + d as x + y > 0.
In similar vein, you can prove all those statements you used.

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