Discrete Math Problems

Section 8.1

#20

Let A={-1,1,2,4} and B={1,2} a,d define relations R and S from A to B as follows: For all (x,y) IN A x B,

x R y <-> |x|=|y| and
x S y <-> x-y is even

Section 8.2

#17
Determine whether the given relation is reflexive, symmetric, transitive or none. Justify.

Recall that a prime number is an integer that is greater than 1 and has no positive integer divisors other than 1 and itself. A relation P is defined on Z as follows: For all m, n IN Z, m P n <-> EXISTS a prime number p such that p|m and p|n.

#26

Let A be the set of all strings of 0's, 1's, and 2's of length 4. Define a relation R on A as follows: For all s, t IN A, s R t <-> the sum of the characters in s equals the sum of the characters in t.

Section 8.3

#19

Prove that the relation is an equivalence relation, describe the distinct equivalence classes of each relation.

F is the relation defined on Z as follows:
For all m, n IN Z, m F n <-> 4|(m-N)

#22

D is the relation defined on Z as follows: For all m, n IN Z,

m D n <-> 3|(m² - n²).

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