709 views

1 Answer

0 votes
0 votes

Answer : C

Given Set $A = \left \{ 1,2,3 \right \}$ and Partial Order relation : $\leq$ (less than or equal to)

So, Hasse diagram will be a Line. Hence, It is a Total Order relation (because Every Two elements are Related) or Chain.

And Every Chain is a Distributive lattice (Because Straight line cannot contain Kite or Pentagon Sublattice ), So, Option C True.

And A Chain is Complemented Lattice only if it has exactly Two elements.

And A Chain is Boolean Algebra only if It has  exactly 2 elements.

NOTE that A Boolean algebra with only one element is called a trivial Boolean algebra or a degenerate Boolean algebra. (Some authors require 0 and 1 to be distinct elements in order to exclude this case.)

Related questions

3 votes
3 votes
1 answer
1
GO Classes asked May 12, 2022
613 views
Assume the following predicate and constant symbols.$W(x,y) :\; x$ wrote $y$$L(x,y) :\; x$ is longer than $y$$h :$ Hardy$a :$ Austen$j :$ Jude the Obscure$p :$ Pride and ...
2 votes
2 votes
1 answer
2
GO Classes asked May 12, 2022
451 views
Let the universe for all quantified variables be the set of all novels. Assume the following predicates and constant symbols:$W(x,y) :\; x$ wrote novel $y$$L(x,y) : \;x$ ...
3 votes
3 votes
1 answer
3
GO Classes asked May 12, 2022
356 views
Working with a unary predicate symbol, $P,$ a binary predicate symbol $Q$ and a unary function symbol $f,$ consider the following interpretation $M,$ given by,Universe $A...
3 votes
3 votes
1 answer
4
GO Classes asked May 12, 2022
318 views
Recall that a "sentence/proposition" is a predicate logic formula that has no free variables.In predicate logic, a set of sentences is satisfiable iff there is some inter...