#### Answer

(a) Since the required speed of a signal is faster than the speed of light, it is not possible that event A caused event B.
(b) Since the required speed of a signal is less than the speed of light, it is possible that event A caused event B.

#### Work Step by Step

(a) We can find the distance between A and B:
$d = 0.4\times 10^8~m - 2~m \approx 0.4\times 10^8~m$
The time difference is $0.2~s-0.1~s = 0.1~s$
Event B occurs $0.1~s$ after event A.
We can find the speed required for a signal to travel from A to B in this time:
$v = \frac{d}{t} = \frac{0.4\times 10^8~m}{0.1~s} = 4\times 10^8~m/s$
Since the required speed of a signal is faster than the speed of light, it is not possible that event A caused event B.
(b) e can find the distance between A and B:
$d = 0.2\times 10^8~m - 2~m \approx 0.2\times 10^8~m$
The time difference is $0.2~s-0.1~s = 0.1~s$
Event B occurs $0.1~s$ after event A.
We can find the speed required for a signal to travel from A to B in this time:
$v = \frac{d}{t} = \frac{0.2\times 10^8~m}{0.1~s} = 2\times 10^8~m/s$
Since the required speed of a signal is less than the speed of light, it is possible that event A caused event B.