Question 1194180
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If 5x-y is divisible by 4 and 2x+3y is odd. Then 7x+2y is odd for all x,y ∈Z. Prove by direct proof or contrapositive
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;To be mathematically correct &nbsp;(and do not scare readers), &nbsp;the statement needs to be &nbsp;<U>modified</U>.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The modified version is &nbsp;THIS :


<pre>
                If x and y are integer numbers such that 5x-y is divisible by 4 and 2x+3y is odd, then 7x+2y is odd.
</pre>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Below is my solution for this modified version.



<pre>
Since 2x + 3y is odd, it means that 3y is odd.


In turn, it means that y is odd.


Next, 5x-y is divisible by 4.  It implies that x-y is divisible by 4.

Since y is odd (see above), it means that x is odd.


Then 7x is odd, and hence 7x + 2y is odd.
</pre>

Proved and solved.