Question

Give a numerical example to show that "a<b and c<d => a-c<b-d" is false.

Answer 1

Let $a=1,\ b=2,\ c=1, \ d=3$ .

Then $a<b$ and $c<d$ , but $a-c>b-d$ , since $0>-1$ .

Therefore, $“a<b,\ c<d\ \Rightarrow \ a-c<b-d”$ is false.