Filtering of a sampled signal Let's say we have 2 signals of frequencies 4 kHz and 8 kHz. 

If we sample both signals with sampling frequency 10 kHz and pass the signal through a low pass filter with cut off frequency of 10 kHz, what frequencies will be present in the output signal?
The 8kHZ signal causes aliasing as we should sample at 2fmax = 2*8kHz = 16kHz (normally we should sample faster than 2fmax). It is also strange that you have 2 signal @4kHz and 8kHz but you want to use a LP at 10kHz.