Trivial (?) Proof

Question

Take, $a$, $b$, $c$, $d$ to be real numbers. If $a>b$ and $c>b$ and $d>b$, can we prove that TECHNICALLY, $a+c>d$, or $a+d>c$, or $c+d>a$. Kind of a brain teaser but I am looking for some honest proof. Thanks.

Answer 1

The claim is false: For example, take

$$a=c=d=-1$$ $$b=-10000$$