Discrete Mathematics Answers

For each of the following sets,

a)     S={1,2,3}, T ={a, b, c}

b)     S={a, b}, T ={1,2,3,4}

c)     S={1,2,3,4}, T ={a, b}

Determine whether

1.     There is a one-to-one function f: S→T;

2.     There is an onto function f: S→T; and

3.     If there is a bijective function f: S→T.

4.     For each (1–3) if such a function exists, explicitly give it. If no function exists give a short explanation?

Let R be a binary relation on N × N defined by (w, x ) R (y, z) if and only if w = y and x ≤ z . Is R reflexive? Is R symmetric? Is R antisymmetric? Is R transitive?

If x and y are not both even numbers, then neither the square of x and y is odd, nor the cube of x and y is even

If A= {1,3,4,6,7} B= {1,2,3,7,6,9,4} C={3,2,7,9,6,1,5,8,4} depict sets A,B and C in a Venn diagram

For each recurrence relation and initial conditions, find: (i) general solution;

(ii) unique solution with the given initial conditions:

(a) an = 3an−1 + 10an−2; a0 = 5, a1 = 11

Ask about the lenght of 5 formed using the lettre ABCDEFG without repetitions. How many string begins with the letter F and end with the letter A

a)     Suppose P (x, y) denotes the equation y=x+8, what will the truth values of the Propositions P (2,2), P (0,4).

If the statement q ^ r is true, determine all combinations of truth values for p and s such that the statement (q -> [¬p v s]) ^ [¬s -> r] is true.

let q(x) denote the statement x is an integer . what are the truth values of the following?

((~a^b)^(b^c)^~b