Kenneth Rosen Edition 7 Exercise 1.7 Question 15 (Page No. 91)

Question

Use a proof by contraposition to show that if $x+y≥2$,where $x$ and $y$ are real numbers, then $x≥1$ or $y≥1$.

Answer 1

Let us assume the contrapositive, i.e both $x,y$ are less than $1$. Now, we are given the fact that $x+y\ge 2$, but from our assumption that  $x<1$ and $y<1$, we get that $x+y<2$ which defies our given fact.