MadeEasy Subject Test: Engineering Mathematics - Lattice

Question

some one please explain how to take the complement in lattice

Comments

To find the complement of any element, calculate glb and lub of this element with other elements say x  and if we get lower bound and upper bound of lattice respectively, then x is the complement of it.
Here the only complement of b is h because
Lub(b, h) = g and Glb(b,h)= c where g is upper bound and c is lower bound of lattice.

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will u explain how u calculate Glb(b,h)=c

thnx

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You can see by looking at hasse diagram to find glb or meet,  both of them meet at 'c'

Glb(a,b) = glb(f,b)= glb(e,b)= glb(d,b) =c

Answer 1

To find a compliment first you have to be clear with Greatest Lower bound GLB and Lowest upper bound LUB.

GLB is a point where two nodes can meet first time in lower direction. (I'm using improper way of explanation but it will be easy).

LUB is a point where two nodes can meet first time in upper direction.

If two nodes are directly joined then GLB is the lower point itself and LUB is the upper point itself. eg GLB(b, i )  = b and LUB(b,i) = i

Now find uppermost and lowermost points of the graph. (uppermost is 'g'  and lowermost is 'c')

Compliment of any node is the point from given node whose GLB and LUB is lowermost and uppermost points of the graph.

Now try to find those points with 'b' whose GLB is 'c' and LUB is 'g'

Here you can find only one point 'h' is satisfying this property.

GLB (b,h) = c (i.e lowermost point of the graph)

LUB (b.h) = g (i.e. uppermost point of the graph)

Hence compliment of a point b is {h} only.

Hope you'll get it :)

Comments

when GLB(b,i)=b and LUB(b,i)=i

how 

GLB (b,h) = c (i.e lowermost point of the graph)

LUB (b.h) = g (i.e. uppermost point of the graph)

can u explain it in little detail

thnx.

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@nikkey123

GLB(b,h): See this as if you want to trace a greatest of the common point at either the same level of lowest(b,h) or below. b & h will find a common point at c which is below the lowest (b,h)

LUB(b,h):See this as if you want to trace a lowest of the common point at either the same level of highest(b,h) or above. b & h will find a common point at g which is above the highest (b,h)