Answer to Question #247661 in Discrete Mathematics for Anirudh

Question

How many subsets of the set {1, 2, 3, 4, 5, 6, 7, 8} do not contain two consecutive integers ?

Answer 1

Subsets not having consecutive integers:

with 4 elements: 2: {1.3.5.7}, {2,4,6,8}

with 3 elements: 10: {1,3,5}, {1,4,6}, {1,3,7}, {1,3,6}, {1,3,8}, {1,4,7}, {1,4,8}, {1,5,7}, {1.5.8},

{1,6,8}

with 2 elements: 21: {1,3}, {1,4}, {1,5}, {1,6}, {1,7}, {1,8}, {2,4}, {2,5}, {2,6}, {2,7}, {2,8}, {3,5}, {3,6},

{3,7}, {3,8}, {4,6}, {4,7}, {4,8}, {5,7}, {5,8}, {6,8}

with 1 element: 8: {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8},

The total number of subsets not having consecutive integers:

$N=2+10+21+8=41$