Discrete Mathematical Structures by Pearson

Solution Manual

Author: Uma Shanker Gupta and ISBN: 978-93-325-2139-1

A-68

(i) To show that B = {1, 2, 3, 4}is a sublattice of A.

Since g.l.b and l.u.b of any two elements of B belong to B, B is a lattice by itself

As B ⊆ A, it is a sublattice of A.

(ii) C = {1, 2, 4, 6} is a sublattice of A proceeding as above in (i).

19. Let A = {a, b, ⊆} and its power set P (A) is a lattice with respect to inclusion relation.

Consider the subset S

1

= {φ, {b}, {c}, {b, c}} of p (A). As the intersection and union of any

two elements of S

1

are their g.l.b and l.u.b belongs to S

1

.

S

2

is a lattice. Since S

1

≤ P (A), it is

a sublattice of P (A).

Now, ...