Proof question, inequalities

Question

Please, I should verify if is truly each supposition, knowing that (a+b)>(d+c), a>b and c>d

1. a>c
2. a>d
3. b>c
4. b>d

That's a problem from my calculus question list. I really need help.

I tried thought induction, with no success.

Answer 1

Only Option 2 is true

Option 1 counterexample: $$a=4,b=3,c=5,d=1$$ Option 3 counterexample: $$a=4,b=3,c=5,d=1$$ Option 4 counterexample: $$a=5,b=1,c=3,d=2$$

Option 2 proof: (where n and m are positive) $$(a+b)>(c+d)$$ $$(a+a-n)>(d+m+d)$$ $$2a>2d+m+n$$ $$2a>2d$$ $$a>d$$