• Attempt any five questions.
• All questions carry equal marks.
List the 16 different relations on the set {0, 1}. How many of the 16 different relations on {0, 1} contain the pair (0, 1). Which of the 16 relations on {0, 1} are reflexive, symmetric and transitive.
Show that the set S = {(1, 3, 5, 7), X₈} forms a group.
Prove that nPₙ(x) = xP'ₙ(x) - P'ₙ₋₁(x) using recurrence relation.
Demonstrate that p∨(q∧r) and (p∨q)∧(p∨r) are logically equivalent. (Using Truth table)
Show that ∼(p∨(∼p∧q)) and (∼p∧∼q) are logically equivalent by developing series of logical equivalence.
Draw the Hasse diagram for divisibility on the set {1, 2, 3, 4, 5, 6}
Define the terms: Abelian Group, Cyclic Group and Normal Sub group.
Discuss various graph terminologies.
What is coloring problem and hence define coloring of graph?
Solve the system by Cholesky decomposition. x + 2y + 3z = 5, 2x + 8y + 22z = 6, 3x + 22y + 82z = -10.
Find the singular value decomposition of the matrix A = [[3, 1, 1], [-1, 3, 1]]
Three samples, each of size 5, were drawn from three uncorrelated normal populations with equal variances. Test the hypothesis that the population means are equal at 5% Level. Sample 1 | 10 | 12 | 9 | 16 | 13 Sample 2 | 9 | 7 | 12 | 11 | 11 Sample 3 | 14 | 11 | 15 | 14 | 16
