GATE CS 2022: Discrete mathematics 2

If the number of elements in a set is ‘n’, then?

Which of the following statements is/are True?
S₁ : In a lattice every two elements need not have both join and meet.
S₂ : In a distributive lattice L, a given element can have atmost one complement.

Condition for monoid is __________

A group (M,*) is said to be abelian if ___________

Consider ‘G’ be a simple graph with 25 vertices and 100 edges. The size of minimum vertex cover is 8. What is the size of maximum independent set of ‘G’?

Consider the following graph:

The chromatic number of the above graph is ________.