Combinatorics | Number Theory Answers

The HCF of two numbers is 11, and their L.C.M is 368. If one number is 64, then the other number is ….

nP8+nP13+nP20+1=nP9+nP15+4 where P means permutations, solve for n?

How many even numbers greater than 5000 are there using digits {1,3,4,5,67}

Compute the sum of all the numbers represented by a 4-bit unsigned binary number.

12. A committee of 3 members is to be formed consisting of one representative each from labor, management,and the public. If there are 3 possible representatives from labor, 2 from management, and 4 from the public, determine how many different committees can be formed?

the electric depot received 108 mp3 players, 12 of which are defective . in how many different ways can 6 players be selected if a) nome are defective b) half are defective c) all are defective

Use Warshall’s algorithm to find the transitive closure of the relation R = {(1,1),(1,4), (2,5),(2,3),(3,1),(3,5),(3,4),(4,2)} on the set A = {1,2,3,4,5}.

Consider the relation R={(a,b)|a divides b} on the set {1,2,3,4,5,6}

(a)List all the ordered pairs in R.

(b) Draw the digraph of R

Find the transitive closure of the relation using Warshall’s algorithm R={(1,2),(2,1),(2,3),(3,4),(4,1)} on the set {1,2,3,4}.

Is the `divides’ relation on the set of positive integers

(a) reflexive? (b) symmetric? (c) transitive? (d) an equivalence relation?

Justify your answers.