Discrete Mathematics Answers

Suppose that P(×) is x² > 1.What is the truth value of Ax P(x) where the universe of discourse consist of all integers?

1. Use the truth tables to verify these equivalence

If A = {1, 2, 3} and B = {4, 5, 6}, state which of the following is a relation from A to B.

(a) R₁ = {(1, 4); (2, 5); (6, 3)}

(b) R₂ = {(2, 5); (3, 6)}

(c) R₃ = {(6, 3); (5, 2); (4, 1)}

(d) R₄ = {(1, 5); (1, 6); (2, 4); (2, 6), (3, 4), (3, 5)}

For the following relation, write an equation that describes the connection between x (the first component in an ordered pair) and y (the second component in an ordered pair).

a. {(1, 1), (1, -1), (4, 2), (4, -2), (9, 3), (9, -3)}

b. {(1, 4), (2, 3), (3, 2), (4, 1), (-2, -3), (6, -1), (7, -2)}

Let R be a relation on the set { a, b, c, d }

R = { (a, b), (a, c), (a, d), (c, b), (c, d), (d, b)}.

Identify the properties satisfied on this given relation.

Consider a relation R on a set A = { 2, 4, 7 }.

Given the relation R = { (2, 2), (2, 4), (2, 7), (4, 7}. Find:

1. Complement of a Relation

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2. Inverse of a Relation

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3. Composite Product R o S and S o R ; S = { (1, 2), (2, 4), (2, 7) }

1. Let S be the set of all strings of English letters. Determine whether these relations are reflexive, irreflexive, symmetric, antisymmetric, and/or transitive.

a) R1 = {(a, b) | a and b have no letters in common}

b) R2 = {(a, b) | a and b are not the same length}

c) R3 = {(a, b) | a is longer than b}

Let a_{k} = 3^{k} + k - 2 for all k \geq 0.

Write down the values of a_{1}, a_{2} and a_{3}.

Write down the values of A(1), A(2) and A(3) defined by the recurrence relation: A(0) = -1, A(k) = 3A(k - 1) - 2k + 7, k \geq 1

Show that A(k) = a_{k} is a solution of the recurrence relation for all values of k \geq 1.