# How are these 2 frequencies aliases of each other?

I'm trying to understand this solved example from a book, given an analog signal $$x(t) = 3\cos(100\pi t)$$. This signal has a frequency of $$50hz$$. If sampled at $$F_S=75Hz$$ ,I obtain the discrete time signal $$3\cos(\frac{2\pi n}{3})$$.

Now I am supposed to find the frequency $$F$$ lying in the range $$0 < F < F_S/2$$ that yields identical samples. Now I get that this frequency will be $$F = 25Hz$$ by using $$f = \frac{F}{F_S}$$.

However, I learnt earlier that this frequency is supposed to satisfy the relation $$F_k = F_o +kF_S$$ for integer values for k, and as it is obvious, there seem to be no integer solutions for this. Where am I going wrong ?

Any help would be appreciated.

Book Reference : https://engineering.purdue.edu/~ee538/DSP_Text_3rdEdition.pdf

Note that the cosine has a positive and a negative frequency component. Consequently, in the range $$[0,f_s/2]$$ you get a component at $$-50\textrm{ Hz}+75\textrm{ Hz}=25\textrm{ Hz}$$.