Question

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

Answer 1

Answer:

See below.

Step-by-step explanation:

( I assume that you know the basics )

6 sets starting with 1 (HAVE consecutive integers for all) -

{1,2} , {1,2,3} , {1,2,3,4} , {1,2,3,4,5} , {1,2,3,4,5,6} , {1,2,3,4,5,6,7}

5 sets starting with 2

{2,3} , {2,3,4} , {2,3,4,5}...{2,3,4,5,6,7}

4 sets starting with 3

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

3 sets starting with 4

{4,5} , {4,5,6} , {4,5,6,7}

2 sets starting with 5

{5,6} , {5,6,7}

1 set starting with 6

{6,7}

No set starting with 7

Total sets HAVING two consecutive integers are 6+5+4+3+2+1+0 = 21. --------2

Total possible sets are 2 to the power 7 = -----1

Do 1 - 2 and get the answer. I mean the number.

THANK YOU.