Question

We consider the sets D = {m, n, p, q} E = {3,6,8} and the relation from D to E.R = {(m, 3), (m, 8), (n, 6), (n, 8) (p, 3), (q, 3), (q, 6)a) List the pairs of D × Eb)R is it a proper subset of D × E? Why ?c)Represent the relation R using a Cartesian network

Answer 1

D= {m, n, p, q}

E= {3,6,8}

a) D x E = { (m, 3), (m, 6), (m, 8), (n, 3), (n,6), (n,8), (p, 3), (p, 6), (p, 8), (q, 3), (q, 6),

(q, 8) }

b) We need to know what a proper subset is.

Proper subset

A proper subset of a set A is a subset of A that is not equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B.

From the above definition, we can say R is a proper subset of D x E because there are element in D x E that is NOT in R.