Math Answers

A retired couple have a fixed income of P3500 per month. Assuming an annual inflation rate of 7%,

what is the purchasing power of their monthly income in 5 years?

Un solde de prix de vente a été consenti aux conditions suivantes :

• Montant : 40 000 $
• Amortissement : 10 ans
• Terme : 24 mois
• Taux d’intérêt : 6 % (capitalisation trimestrielle)
• Versement : mensuel
• Déterminez les obligations résultant de ce solde de prix de vente.

A sale price balance has been granted on the following conditions: amount: $40,000; amortization: 10 years; term: 24 months; interest rate: 6% (a quarterly compounding); installment: monthly. Determine the obligations resulting from this sale price balance.

Question 2: Give an example of each of the following graph containing:

i.An Euler circuit but not Hamiltonian cycle

ii.A Hamiltonian cycle but not an Euleriancircuit

iii.An Eulerian circuit as well as Hamiltonian cycle

Question 2: Define Hamiltonian circuit and Euler circuit. Give an example of each of the following graphs

i.N-Cube (Q₃)

ii.Complete Bipartite

iii.Regular graph of degree 4

iv.Cycles graph (C4, C₅)

v.Wheels graph (W₄ ,W₅)

vi.Hamiltonian, but non- Eulerian

vii.Eulerian but non-Hamiltonian

viii.Eulerian as well as Hamiltonian.

Question 2: Let R be a relation in a set A, and derive from R another relation S in A as follows:

x S y if (x R y xor y R x).

Recall that xor, exclusive or, is defined as: p xor q is true if (p is true and q is false, or p is false and q is true).

a) Prove that S is irreflexive.

b) Prove that S is symmetric.

Question 1: Let R be a relation in a set A, and derive from R another relation S in A as follows:

x S y if (x R y or y R x).

a) Prove that if R is reflexive, then S is reflexive.

b) Prove that S is symmetric.

c) Prove that if R is transitive, S is not necessarily transitive (by a counterexample).

d) If R is antisymmetric, is S antisymmetric? Prove your answer.

e) If R is an equivalence relation, is S an equivalence relation? Prove your answer.

f) If R is a partial order, is S a partial order? Prove your answer.