Show that if a, b e z, then a^2 - 4b =/ 2

Step-by-step explanation:

Proposition If a, b , then

You can prove this proposition by contradiction, you assume that the statement is not true, and then show that the consequences of this are not possible.

Suppose the proposition If a, b , then is false. Thus there exist integers If a, b for which

From this equation you get so is even. Since is even, a is even, this means for some integer d. Next put into . You get so . Dividing by 2, you get . Therefore , and since , it follows that 1 is even.

And that is the contradiction because 1 is not even.  In other words, we were wrong to assume the proposition was false. Thus the proposition is true.

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8