Math Answers

{F} Construct a relation on the set {a, b, c, d} that is a. reflexive, symmetric, but not transitive. b. irreflexive, symmetric, and transitive. c. irreflexive, antisymmetric, and not transitive. d. reflexive, neither symmetric nor antisymmetric, and transitive. e. neither reflexive, irreflexive, symmetric, antisymmetric, nor transitive.

{F} Let R1 and R2 be symmetric relations. Is R1 ∩ R2 also symmetric? Is R1 ∪ R2 also symmetric?

{F} LA. find the minimal polynomial of the linear operator t : R³ "- R³" define by t (x,y,z) =(x+2y+3z, 4y+5z,6 z).is t

{F} Determine the length of the parametric curve given by the following parametric equations. x=3sin(t) y=3cos(t) 0<t<2π

{F} The furniture company inexpensive tables and chairs. The production process of each is similar in the painting department each table take 4 hours of carpentry and 2 hours in the painting department. Each chair requires 3 hours of carpentry and 1 hour painting department. During the current product period 240 hours of carpentry time are available and 100 hrs in the painting is available. Each table sold yields of profit of $7 and chair produced sold for $5 profit. Find the best combination of table and chairs to manufacture in order to reach the maximum number of profit?

{F} Define and give examples of injective surjective and bijective functions. Check the injectivity and surjectivity of the following function f: NN given by f(x)=x2

{F} Show that the following logical equivalences hold for the

Peirce arrow ↓, where P ↓ Q ≡ ∼(P ∨ Q).

a. ∼P ≡ P ↓ P

b. P ∨ Q ≡ (P ↓ Q) ↓ (P ↓ Q)

c. P ∧ Q ≡ (P ↓ P) ↓ (Q ↓ Q)

H d. Write P → Q using Peirce arrows only.

e. Write P ↔ Q using Peirce arrows only.

{F} How many different sequences, each of length r, can be formed using elements

from A if

(a) elements in the sequence may be repeated?

(b) all elements in the sequence must be distinct?

an + an-1 - 10an-2 + 8an-3

1. a metal washer 1 inch. in diameter is pierced by a 1/2 - inch hole. what is the area of one of the washer?
2. the vertical end of a trough has the following dimensions width at top 4.4ft., width at bottom 3.2ft., depth 3.5ft. find the area of the end of the trough.
3. the surface of hemispherical dome whose diameter is 36ft. is to be covered with gold leaf which costa 15 cents per square inch. what must be paid for the golf leaf?
4. a cubic foot of ivory weighs 114Ib. find the weight of 1000 ivory billiard balls 21 in. in diameter?

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