Discrete Mathematics Answers

Let A= {1,2,3,4,6,9,12} let a R b if a is divided by b. Show that R is POSET, Draw Hasse Diagram. Prove or disprove if it is a Lattice.

Let A= {1,2,3,4,5,6} and R be a relation on A, such that
R = [(x, y): |x-y| =2]. Use warshall’s Algorithm to find the matrix of transitive closure of R. and draw its digraph

Let A= {1,2,3,4,5,} and R be a relation on A, such that
R = [(1,4), (2,2), (3,4), (3,5), (4,1), (5,2), (5,5)]. Use warshall’s Algorithm to find the matrix of transitive closure of R

If A={1,2,3,6,12,18,24,30,36,150} and the partial ordering relation is divides then draw the hasse diagram

For every integer n≥1,(n3+11n)⋅(8n−14n+27) is divisible by

6


7


42


84

Define the relation of d on A by xdy if x is contained within y. For
example, 01d101. Draw a digraph for this relation.

Let F(x, y) be the statement "x can fool y," where the domain consists of all people in the world. Use quantifiers to express each of these statements.

A box contains 6 white balls and 6 black balls. Find number of ways 4 balls can be
drawn from the box if
i) Two must be white
ii) All of them must have same color

Out of 5 male and 6 female a committee of 5 is to be formed. Find the number of ways
in which it can be formed so that among the person chosen in the committee there are:
i) exactly 3 males and 2 females
ii) at least 2 males and one female