Tit, Tut, Tet, Tot

Level pending

Defined that \(tit, tut, tet\) and \(tot\) are sets which have these following properties:

  1. Not all sets are disjoint
  2. Intersection of the joint sets have 9 elements
  3. 14 elements only belong to \(tit\), meanwhile \(tot\) has 22 elements in total
  4. \(Tut\) has two elements more than \(tot\) does
  5. \(Tit\) and \(tut\) intersect each other with 10 elements included
  6. Twice the number of elements the intersection of the joint sets have are \(tut's\) but also belong to other two sets
  7. Every \(tet\) is \(tit\), but 16 of \(tit's\) aren't \(tet's\). An eighth of this quantity is \(tit's\) and \(tot's\) at once, but not \(tut's\)

If \(tet\) has 10 elements and the universe equals to the four elements. How many elements are there?

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