Homework Sourse1 Four sets A1 A2 A3 A4 have the property that Ai Aj Ak
1. Four sets A1, A2, A3, A4 have the property that Ai ? Aj ? Ak = ? whenever i, j, k are distinct. In addition, |Ai ? Aj| = 1 whenever i ? j and |Ai| = 5 for all i. Find the number of elements that belong to at least one of the sets.
Solution
5+5+5+5-1-1-1-1-1-1=14.
It is calculated using the following formula. Some terms are 0. \\(|A1\\cup A2\\cup A3\\cup A4|=|A1|+|A2|+|A3|+|A4|-|A1\\cap A2|-|A1\\cap A3|-|A1\\cap A4|-|A3\\cap A2|-|A4\\cap A2|-|A3\\cap A4|\\)
