Choose the main technique to prove the following statement.

√3√3\sqrt{3} is irrational.

Choose the main technique to prove the following statement:

x2+2x−8=0x2+2x−8=0x^2 + 2x -8=0 has integer solutions.

Choose the main technique to prove the following statement.

If nnn is even, then 5n2+6n+75n2+6n+75n^2+6n+7 is odd.

Choose the main technique to prove the following statement.

If 5n2+6n+75n2+6n+75n^2+6n+7 is odd, then nnn is even.

Consider a function f:R→Rf: R \to R, f(x)=x2f(x) = x^2.

Determine the correct sequence to prove the following statement. 

ff is not injective.

If a statement is not used in the proof, you have to choose "Not used".

Consider a function f:R→Rf:R→Rf: R \to R, f(x)=2x+8f(x)=2x+8f(x) = 2x+8.

Determine the correct sequence to prove the following statement. 

fff is surjective.

If a statement is not used in the proof, you have to choose "Not used".

Consider a function f:R→Rf: R \to R, f(x)=x2f(x) = x^2.

Determine the correct sequence to prove the following statement. 

ff is not surjective.

If a statement is not used in the proof, you have to choose "Not used".

Consider a function f:R→Rf: R \to R, f(x)=2x+8f(x) = 2x+8.

Determine the correct sequence to prove the following statement. 

ff is injective.

If a statement is not used in the proof, you have to choose "Not used".

Find the correct answer for the following expression.

The ceiling of -6.8

Find the correct answer for the following expression.

The ceiling of 1.6