What is a lattice, Mathematics

Assignment Help:

What is a lattice? Which of the following graphs are lattice and why?

Ans:  Let (L, ≤) be a poset. If each subset {x, y} consisting of any two elements of L, comprises a glb (Infimum) and a lub (Supremum), then the poset (L, ≤) is known as a lattice. A glb ({x, y}) is denoted by x∧y and it is called meet of x and y. Likewise, lub ({x, y}) is denoted by x∨y and it is called join of x and y. Hence, lattice is a mathematical structure equipped along with two binary operations meet and join. 

 

1127_What is a lattice.jpg

In the specified examples, (a) is a lattice as each pair of elements has a meet and join in the set within the relation denoted by the graph. Graph in (b) does not denote a lattice as bottom two elements comprise no meet and top two elements have no join. 

In the case of (c), the relation denoted is not even anti symmetric as two bottoms and two top level elements are at similar level and denoted as related to each other (symmetric) with no being similar element (equal).


Related Discussions:- What is a lattice

Determine the conditional probability, Consider a class of 55 students. The...

Consider a class of 55 students. The student names are placed in a hat and 3 names are randomly drawn without replacement. a) If the first person drawn was named the class presi

Determine the optimal strategy, On a picnic outing, 2 two-person teams are ...

On a picnic outing, 2 two-person teams are playing hide-and-seek. There are four hiding locations (A, B, C, and D), and the two peoples of the hiding team can hideseparately in any

COS Sheets, How do I find percentages with doing COS Sheets

How do I find percentages with doing COS Sheets

#rounding off, I am the least two digit number which round off to 100?

I am the least two digit number which round off to 100?

Simplification, how do we answer questions with fraction mixed. what are th...

how do we answer questions with fraction mixed. what are the easier ways to do it

Determine the quotient and remainder , Let a = 5200 and b = 1320. (a) If...

Let a = 5200 and b = 1320. (a) If a is the dividend and b is the divisor, determine the quotient q and remainder r. (b) Use the Euclidean Algorithm to find gcd(a; b). (c)

Calculate the area and perimeter of a right triangle, Calculate the area an...

Calculate the area and perimeter of a right triangle: Calculate the area and perimeter of a right triangle with a 9" base and sides measuring 12 and 15.  Be sure to involve th

NCCER, what is 9/16 Divided by 7/8

what is 9/16 Divided by 7/8

Linear equations in one variable, three prices are to be distributed in a q...

three prices are to be distributed in a quiz contest.The value of the second prize is five sixths the value of the first prize and the value of the third prize is fourfifth that of

Ratios, the ratio of boys to girls in the sixth grade is 2:3 if there are ...

the ratio of boys to girls in the sixth grade is 2:3 if there are 24 boys, how many are girls?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd