Question 1208936
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Answer: <font color=red size=4>False</font>


Explanation
x = rational number
y = irrational number
x = a/b for some integers a,b where b is nonzero
y cannot be written as a fraction of integers because it is set up to be irrational.


Assume x+y was rational. 
We'll do a proof by contradiction to show that x+y is instead irrational.
x+y = rational
x+y = p/q
(a/b) + y = p/q
y = (p/q) - (a/b)
y = (bp)/(bq) - (aq)/(bq)
y = (bp-aq)/(bq)
y = (some integer)/(some integer)
y = rational number
But wait, we made y irrational and now it's rational. 
This is clearly a contradiction.

 
A number cannot be both rational and irrational at the same time. 
The term "irrational" literally means "not rational". 
This contradiction means the assumption x+y = rational is false, so x+y = irrational must be the case.


A template to write down in your notes would be <font color=blue>rational + irrational = irrational</font>
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