Previous year Discrete mathematics question paper- GATE 2025 Lattices The following is the hasses.

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:

1. The least upper bound (LUB) of ‘a’ and ‘x’ is the greatest element (often denoted as ‘1’ or ‘I’).
2. 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.