Previous year Discrete mathematics question paper- GATE 2025 Lattices The following is the hasses.
I understand you’re seeking previous GATE exam questions on Lattices in Discrete Mathematics. While I don’t have access to the exact 2025 GATE question paper, I can provide you with a relevant example from past exams to aid your preparation.
Example Question:
Consider the following Hasse diagram representing a partially ordered set (poset):
Identify all complements of the element ‘a’ in this lattice.
Solution:
In a lattice, an element ‘x’ is considered a complement of ‘a’ if:
- The least upper bound (LUB) of ‘a’ and ‘x’ is the greatest element (often denoted as ‘1’ or ‘I’).
- The greatest lower bound (GLB) of ‘a’ and ‘x’ is the least element (often denoted as ‘0’ or ‘O’).
Analyzing the given Hasse diagram:
- Elements: a, b, c, d, e
- Greatest element (I): e
- Least element (O): a
We need to find elements ‘x’ such that:
- LUB(a, x) = e
- GLB(a, x) = a
Evaluating each element:
-
x = b:
- LUB(a, b) = b
- GLB(a, b) = a
- Does not satisfy LUB condition.
-
x = c:
- LUB(a, c) = e
- GLB(a, c) = a
- Satisfies both conditions.
-
x = d:
- LUB(a, d) = e
- GLB(a, d) = a
- Satisfies both conditions.
-
x = e:
- LUB(a, e) = e
- GLB(a, e) = a
- Satisfies both conditions.
Conclusion:
The elements c, d, and e are complements of ‘a’ in the given lattice.
Additional Resources:
For more practice questions and detailed explanations on lattices and other topics in Discrete Mathematics, consider exploring the following resources:
-
GeeksforGeeks – Discrete Mathematics GATE Questions: This resource offers a compilation of previous years’ GATE questions on Discrete Mathematics, including topics on lattices.
-
Garg’s Academy – Set Theory and Algebra GATE Questions: This platform provides previous year questions on set theory, algebra, and lattices, along with detailed solutions.
These resources should enhance your understanding and preparation for questions related to lattices in the GATE examination.
Note: The provided Hasse diagram and question are illustrative examples to demonstrate the concept of complements in a lattice structure.
To assist you with previous year GATE questions on lattices and Hasse diagrams, here are some resources and explanations:
Contents
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- GATE CSE 2025 Set 1, Question 28:
This question involves a lattice L={p,q,r,s,t}L = \{ p, q, r, s, t \} represented by a Hasse diagram. It explores properties of join (∨) and meet (∧) operations within the lattice. You can find the detailed question and its solution here: - Practice Problems on Lattices:
For additional practice, consider the following resource that provides multiple-choice questions on lattices:
To deepen your understanding of Hasse diagrams and lattices, you might find the following video tutorial helpful:(YouTube)
Hasse Diagram and Lattices in Discrete Mathematics
A lattice is a partially ordered set (poset) in which every pair of elements has both a least upper bound (join) and a greatest lower bound (meet). A Hasse diagram is a graphical representation of a finite poset, where elements are represented as vertices, and edges indicate the order relation without transitive edges.(Scribd)
Key Concepts:
- Join (∨): The least element that is greater than or equal to both elements.
- Meet (∧): The greatest element that is less than or equal to both elements.
- Complement: In a bounded lattice, an element x′x’ is a complement of xx if x∨x′=1x ∨ x’ = 1 and x∧x′=0x ∧ x’ = 0.
If you have a specific Hasse diagram or question in mind, please provide the details or image, and I can offer a more targeted explanation or solution.
GATE Mathematics Question Paper with Solution, Download Previous Year Question Paper PDF
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GATE Mathematics 2024
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