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Combining Inequalities

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Combining Inequalities

by birdpoop » Sun Oct 05, 2008 5:57 pm
For those of you familiar with Manhattan's LI/CH/LU/C technique for combining inequalities, why is that when combining (C) you have to take the upper and lower extremes? For example:

If x > 8, x < 17, and x < 14, the combined statement should be:

8 < x < 14

Why will you miss a problem if you don't take the extremes?

Thanks.
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by stop@800 » Sun Oct 05, 2008 9:01 pm
I am not familiar with manhattan rules
but from your explanation I can guess a little about those
so here goes my answer

x<14 and x<17

we need to find all values of x that satifies these two conditions
x<14
means x lies from -infinity to 13, inclusive [if x is integer]

x<17
means x lies from -infinity to 16, inclusive [if x is integer]

now we ned intersection of both
that is values which are satisfied for both
range is
means x lies from -infinity to 13, inclusive [if x is integer]
so x<14

Hope this helps!!
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