Independent events from their union and intersection

Events \(A\) and \(B\) are independent, with \(\mathrm{P}(A\cap B)=0.12\) and \(\mathrm{P}(A\cup B)=0.58\).

1. Show that \(\mathrm{P}(A)\) and \(\mathrm{P}(B)\) are the roots of the equation \(t^2-0.7t+0.12=0\). Hence find \(\mathrm{P}(A)\) and \(\mathrm{P}(B)\), given that \(\mathrm{P}(A)>\mathrm{P}(B)\).[4]
2. Find \(\mathrm{P}(A\mid A\cup B)\).[2]
3. Show that there are no two independent events \(C\) and \(D\) with \(\mathrm{P}(C\cap D)=0.35\) and \(\mathrm{P}(C\cup D)=0.8\).[3]