Does $1-ab\geq (1-a)(1-b)$ hold, for $a,b\in [0,1]$? Does this inequality hold, for any $a,b\in[0,1]$
$$1-ab\geq (1-a)(1-b)?$$
I'm don't have idea to conclude $1-ab\geq 1-a-b+ab = (1-a)(1-b)$.
Anyone can prove (or disprove) it?

$1-ab \ge 1-a \ge (1-a)(1-b).\blacksquare$

Update: I found this is equivalent to that of @Albus Dumbledore and @Tony Ip.
