# ExampleI - divisible by 5 and 11 5 divisible by 11 but not...

This preview shows page 1. Sign up to view the full content.

DISCRETE MATHEMATICS Example 1. How many bits strings are there of length six or less? 2. How many positive integers less than 1000 are 1. divisible by 7, 2. divisible by 7 but not by 11, 3. divisible by neither 7 nor 11. 3. How many positive integers less than 1000 are 1. divisible by 5, 2. divisible by 5 but not by 9, 3. divisible by neither 5 nor 9. 4. How many ordered pairs of integers (a, b) are needed to guarantee that there are two ordered pairs (a 1 , b 1 ) and (a 2 , b 2 ) such that a 1 mod 3 = a 2 mod 3 and b 1 mod 3 = b 2 mod 3? 5. How many subsets with an odd number of elements does a set with 10 elements have? 6. How many positive integers less than or equal to 5000 that are 1. divisible by 11, 2. divisible by 5 but not by 11, 3. divisible by neither 5 nor 11, 4.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: divisible by 5 and 11, 5. divisible by 11 but not by 5? 7. How many subsets of a set with 20 elements have more than one elements? 8. How many bit strings of length n are palindromes? (A palindrome is a string whose reversal is identical to the string itself.) 9. How many bit strings of length 10 either begin with three 0s or end with two 0s? 10. How many positive integers between 100 and 999 (including 100 and 999) are there that are divisible by 4 but not by 3? 11. How many bits strings are there of length five or less excluding empty bit string? 12. How many postive integers less than 500 are 1. divisible by 9, 2. divisible by 9 but not by 5, 3. divisible by neither 9 nor 5....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online