What is A1 and A4 licencing in retail?

Each of the 4 sets A1, A2, A3, and A4 contains 4 elements. The intersection of every i of these 4 sets?

• Each of the 4 sets A1, A2, A3, and A4 contains 4 elements. The intersection of every i of these 4 sets (2 less than or equal to i less than or equal to 4) consists of 5-i elements. What is |A1 union A2 union A3 union A4|?

• Answer:

  Every pair has 3 elements in common Every trio has 2 elements in common Every quad has 1 element in common A1 = (a b c d) A2 = (a b c e) A3 = (a b d e) A4 = (a c d e) Intersections: quad: (a) trios: 1,2,3: (a,b) 1,2,4: (a,c) 1,3,4: (a,d) 2,3,4: (a,e) pairs: 1,2: (a,b,c) 1,3: (a,b,d) 1,4: (a,c,d) 2,3: (a,b,e) 2,4: (a,c,e) 3,4: (a,d,e)