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Let A = {1, 2, 3) and B = {a, b, c). Let R = {(1.b)(1.c)(3.b)}. Find the domain and range of the relation. Determine ..

Let D denote the set of all positive divisors of the positive integer n. Determine and represent it by Hasse Diagram.

Define isomorphic and Hamilton Graphs with example.

Let f, g, be functions from N to N (set of natural numbers) for such that f(n) = n + 1, g(n) = 2n. Find fog and gof.

Define Tautology and contradictions,

Show that the relation of parallel lines in the set of lines on a plane is an equivalence relation.

Choose any two statements p and q as you like. Draw the truth table for and

Consider the graph G (V, E) where v consists of Four vertices A, B, C,D and E of five edges where represent this undirected graph diagrammatically. Determine the degree of each vertex.

Let f be a mapping from R to R such that f(x) = 2x + 3. Show that f is invertible and find its inverse.

.If n (A) = 40, n(B) = 30, = 20. Then find

Let A = {1,2,5,6), B = {2,5,7), C = (1,3,5,7,9).Verify (A x B) {A X C} = A x B x C}.

Let N = {1,2,3,........), denote the set of all positive integers and A = {, 3 < x < 12), B = {, x is even, x < 15). Find

If R is an equivalence relation in a set A. Then prove that is also equivalence relation.

In a lattice, prove that

Define complemented lattice, also find the complement (if exists) of all elements of

Let A = {1,2,3,4,6,8,9, 12, 18, 24} be equipped with relation x divides y.Draw the Hasse diagram.

Let G be an undirected graph with m vertices, sayDefine the adjacent matrix A of G. Consider the undirected graph G with 5 vertices shown in the following diagram.

Draw the directed graph for the following incident matrix. Also find the degree of all vertex.

Show that the two graphs shown in the figure are Isomorphic.

Prove that the union of two graphs will be a graph such that.

By means of truth tables, justify that the conditional statement "If p then q" is logically equivalent to the statement "Not p or q".

Define a proposition. Let p and q be propositions and denote compound proposition, "if p then q" Draw the truth table for the compound proposition Let p: you try, and q: you will succeed. Justify the truth table for

Verify De-morgan's laws for propositions. And also prove that.

Consider the following:P: Today is Tuesday, Q: It is raining, R: It is cold.Write in simple sentence the meaning of

Consider the following:P: Today is Tuesday, Q: It is raining, R: It is cold.Write in simple sentence the meaning of .

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