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we are given the following constraints for x $$x \le e+f-a$$ $$x \le z+f-c$$ $$x \le e+y-b$$ $$d \le b+c-a$$

We need to prove(or disprove) that

$$x \le z+y-d$$ where $x, y, z, a, b, c, d, e \in \mathbb{R}$ I tried for some examples and it seems that the relation to be shown holds given the constraints. But I don't know the formal way of proving. Any starting point, hint will be helpful.

punter147
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  • Pick numbers for $x,y,z,d$ that make the inequality false and then try and fill in the gaps for the other variables to make sure all the constraints are still true. – Highlander13 Oct 23 '21 at 11:23
  • Take $x=0$, $y=1$, $z=-2$, $a=1$, $b=2$, $c=0$, $d=0$, $e=1$ and $f=2$. – mathlove Oct 23 '21 at 12:52

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