## Fill-in-the-blank proofs
for Section 2.5

**Claim:**
If an integer *n* has the form 3*K* + 1, then *n* does
not have 9*L* + 5.

*Proof by contradiction*.* *Click
here.

**Claim:**
For all real numbers *x* and *y*, either *x* ≥ (*x*
+ *y*)/2 or *y* ≥ (*x* + *y*)/2.

*Proof by contradiction*.* *Click
here.** **

** Claim:**
For every integer* n*, if *n*^{2} is even, then *n*
is even.

* Proof by contradiction*.* *Click here.

**Claim:**
For every integer* n*, if *n*^{2} is odd, then *n*
is odd.

* Proof by contradiction*.* *Click here.