Answer
Proof by contraposition below to show that if $x+y\geq 2, x, y\in \mathbb{R},$ then $x\geq 1$ or $y\geq 1$.
Work Step by Step
We want to show that if $x+y\geq 2$, with $x, y\in \mathbb{R}$, then $x\geq 1$ or $y\geq 1$. To do so with a proof by contraposition, we assume both $x<1$ and $y<1$. If this is the case, then $x+y<1+1=2$. Because $x+y$ is not greater than or equal to 2 if neither $x$ nor $y$ is greater than or equal to 1, our statement is proved.
