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Determine whether the below Hasse diagram represents a lattice

written 9.0 years ago by teamques10 ★ 70k

modified 3.9 years ago by krithikkm200 • 10

Mumbai University > Computer Engineering > Sem 3 > Discrete Structures

Marks: 6 Marks

Year: Dec 2015

discrete mathematics

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written 9.0 years ago by teamques10 ★ 70k

•   modified 9.0 years ago

By lattice definition we can prove the above shown structure $M_9$ to be a lattice if and only if $∀x,y∈M_9$, {x,y} has supremum and infimum in $M_9$. Putting all such subsets in a table, not mentioning those subset where x=y:

Subset	x ^ y	x V y
{a, b}	a	b
{a, c}	a	c
{a, d}	a	d
{a, e}	a	e
{a, f}	a	i
{a, g}	a	i
{a, h}	a	h
{a, i}	a	i
{b, c}	a	h
{b, d}	a	g
{b, e}	b	e
{b, f}	b	f
{b, g}	a	i
{b, h}	b	h
{b, i}	a	i
{c, d}	c	d
{c, e}	c	f
{c, f}	c	f
{c, g}	c	g
{c, h}	c	h
{c, i}	c	i
{d, e}	a	i
{d, f}	d	i
{d, g}	d	g
{d, h}	d	g
{d, i}	d	i
{e, f}	e	f
{e, g}	e	i
{e, h}	e	f
{e, i}	e	i
{f, g}	f	i
{f, h}	h	f
{f, i}	f	i
{g, h}	h	g
{g, i}	g	i
{h, i}	h	i

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