// Problem 4.6
let isValid ((bnsman , bnsopt), (tcman, tcopt), (ppsman, ppsopt), ep) cb =
    let bns = Set.union bnsman bnsopt
    let tc = Set.union tcman tcopt
    let pps = Set.union ppsman ppsopt
    let bnstc = Set.intersect bns tc
    let bnspps = Set.intersect bns pps
    let tcpps = Set.intersect tc pps
    let allSets = Set.union (Set.union bnstc bnspps) tcpps
    let elective = Set.forall ep allSets
    isValidCourseGroup (bnsman, bnsopt) cb && isValidCourseGroup (tcman, tcopt) cb && isValidCourseGroup (ppsman, ppsopt) cb && Set.isEmpty ( Set.union (Set.union bnstc bnspps) tcpps ) && elective;;