Discrete Mathematics Answers

Solve the congruence 5x≡1(mod12)

Hint: 0≤x≤11

A particular algorithm increases in time as the number of operations, n, increases.

Suppose the time complexity of this algorithm is given by: f(n) =4n³+5n² * log(n).

Show that f(n) is O(g(n)) for g(n) = n³.

a particular algorithm increases in time as the number of operations n increases.

Suppose the time complexity of this algorithm is given by:

f(n)=4n²+5n²*log(n)

Show that f(n) is O(g(n)) for g(n) = n³

Show that x² is not O(x*log(x))

The rational numbers with 17 as a denominator are ...

a) finite

b) countably infinite

c) uncountable

d) non of these

Choose 1 answer

Fourteen chess players a, b, c, d, e, f, g, h, i, j, k, l, m, n are to be paired so they can play 7 games starting at the same time. The only pairs allowable are the following: {c,f}, {a,d}, {b,g}, {e,h}, {a,i}, {a,j}, {a,k}, {a,l}, {a,m}, {a,n}, {b,h}, {b,j}, {b,k}, {b,l}, {b,m}, {b,n}, {c,i}, {c, j}, {c,k}, {c,l}, {c,m}, {c,n}, {d,h}, {d,i}, {d,j}, {d,k}, {d,l}, {d, n}, {e,h}, {e,i}, {e,k}, {e,l}, {e, m}, {e, n}, {f,i}, {f,j}, {f, k}, {f,l}, {f,m}, {f,n}, {g,i}, {g,j}, {g,k}, {g,l}, {g,m}, {g,n}, {h,i}, {h,j}, {h, m}. Find a possible pairing.

Find a system of distinct representatives for the following sets: {b,e,i,l}, {a,j,m}, {c,f,k}, {b,h,i,l}, {d,g,m}, {e,h,k,l}, {a,d,j}, {g,j,m}, {c,e,k}, {a,g,j}, {f,h,i}, {d,j,k,m}, {b,c,f}.

Find a system of distinct representatives for the following sets: {a, c, f}, {b, g}, {c, d, h}, {a, d, j}, {e, i, k}, {f, j, l}, {b, i, k}, {e, g}, {a, c, f, h, l}, {g, k}, {b, e, i}, {d, h, j}. 

Determine the number of bijective functions f from {1, 2, . . . , 8} to itself such that f(i) 6= i for any even number i.

Determine the number of subsets of size k of the set {1, 2, . . . , n} which do not contain consecutive integers.