Find intersection measure of a probability space

I have that $(X,mathbf{A},mu)$ is a probability space and $A,B in mathbf{A}$ with $mu(A)=frac{5}{12}$ , $mu(B)=frac{1}{2}$ and $mu((Acup B)^{c}) = frac{1}{4}$.

I would like to find $mu(Acap B )$.

Is it correct to calculate that $mu(Acup B) = 1 – mu((Acup B)^{c}) = 1 – frac{1}{4} = frac{3}{4}$?

And then use the fact that $mu(Acup B) + mu(Acap B) = mu(A) + mu(B)$ to find that
$mu(Acap B) = mu(A) + mu(B) – mu(Acup B) = frac{5}{12} + frac{1}{2} – frac{3}{4} = frac{1}{6}$ ?

I’m not sure about this so any input would be much appreciated!