Let \(\boldsymbol{A}\) and \(\boldsymbol{B}\) be events with \(P\{\boldsymbol{A}\}=1 / 2, P\{\boldsymbol{B}\}=1 / 3\), and \(P\{\boldsymbol{A} \cap \boldsymbol{B}\}=\) \(1 / 4\). Find

(a) \(P\{\boldsymbol{B} \mid \boldsymbol{A}\}\),

(b) \(P\{\boldsymbol{A} \mid \boldsymbol{B}\}\), and

(c) \(P\{\boldsymbol{A} \cup \boldsymbol{B}\}, P\left\{\boldsymbol{A}_{c} \mid \boldsymbol{B}_{c}ight\}\), and \(P\left\{\boldsymbol{B}_{c} \mid \boldsymbol{A}_{c}ight\}\). Here, \(\boldsymbol{A}_{c}\) and \(\boldsymbol{B}_{c}\) are the complements of \(\boldsymbol{A}\) and \(\boldsymbol{B}\), respectively.