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1. Use a counter example to disprove this statement X < 3 implies x^2 < 9

2.prove that n^2 + n + 41 does not take prime values for all positive integers 

3. Are any two straight lines that never meet necessarily parallel 

 Oct 31, 2018
 #1
avatar+420 
+2

well I can't answer the other two but I can answer the last one 

 

if two lines are not parallel they will meet at some point because a line goes at both directions at an infinite scale and sooner or later they will meet the only exception is when your dealing with a ray a line that starts at a point and goes on in one direction at an infinite scale

 

I hope this was helpful 

 Oct 31, 2018
edited by DarkCalculis  Oct 31, 2018
 #2
avatar+18360 
+2

The first one is UNtrue because, what if x is less than negative three?

 Oct 31, 2018
 #3
avatar+100579 
+1

First one

Let x  = -4

So  (-4)^2  =  16

So....x^2 > 9

 

Second one

 

Let n = 41

So

41^2 + 41 + 41      =  41 ( 41 + 1 + 1)   =   43 *41  so...it is not prime 

 

Last one

 

In "three-space," we can have two lines that never meet but are not parallel....these are known as "skew" lines

 

 

cool cool cool

 Oct 31, 2018

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