Other Math Answers

Find the distance of the linear code C with the given generator matrix

G=1 1 1 0 0 0 0 0 00 0 0 1 1 1 0 0 01 1 1 1 1 1 1 1 1

Find the generator matrix for C andC where H=100100010001010001

Use matrix method to solve  d2x/dt^2 +4x+2. X(0)=1 x'(0) = 0 (CO6)

A pile driver of mass 180 Kg falls freely through a distance of 6 metres to strike a pile of 500 Kg and drive it 100mm into the ground. The hammer does not rebound when driving the pile.

Determine the average resistance of the ground

solve the problem in two ways.

a)  By making use of the principle of conservation of momentum and D’Alembert’s principle.

b ) By making use of the principle of conservation of energy.

1. According to Dedekind’s definition, are N, Z, and Q infinite sets? Explain.

2. Compare Cantor’s and Dedekind’s definitions.

E. Determine the truth value of the compound statement given that p is a false statement, q is a true statement, and r is a true statement

1. p ν ( ~q ν r)

2. r ^ ~(p ν r)

F. Use two truth tables to show that each of the statements are equivalent.

1. p ν( p ^ r ) Ξ p

2. p ν(q ^ ~p) Ξ p ν q

G. Use a truth table to determine whether the given statement is a tautology or a self contradiction.

1. p ν~ p

2. p ^ (~p ^ q

Answer the following. Write your complete solution in a separate sheet of paper.

1. Let P = I played tennis this morning, and Q = I went swimming this afternoon.

Interpret each of the following:

a. P V Q c. P Λ Q e. ~( P V Q)

b. P V ~Q d. ~ P V Q f. ~( P Λ Q)

2. Set up truth tables for (p V q) and (p V q). Where do they differ?

3. Show that (p V q) <=> [(p V q) Λ ~(p Λ q)].

In Nos. 4 -5, use Theorems 11 and 12 to formulate (in good English) the negation of each of the compound sentences.

4. I had a sandwich and a cup of coffee.

Use truth tables in Nos. 1 – 6.

1. Prove (p Λ p) <=> p. 4. Prove [(p Λ q) Λ r] <=> [p Λ (q Λ r)].

2. Prove (~p) <=> [~(~(~p))]. 5. If s<=> t, show that t <=>s.

3. Prove (p Λ q) <=> (q Λ p). 6. If s <=> t and t <=> u , show that s <=>u.

7. A young man received the following note from his girlfriend. "Dear Fred, I want to explain that I was really joking when I told you that I didn’t mean what I said about reconsidering my decision not to change my mind.” Did she finally change her mind or didn’t she? [Hint: Let P = “She changed her mind.” Apply Theorem 1 to [~(~(~(~(P))))].

8. In what context may the sentence, “Mr. Jones is the father of my best friend,” be considered to be equivalent to the sentence, “My best friend is a son of Mr. Jones.” Under what circumstances are these two sentences not equivalent?