How many distinguishable permutations can be made of the

Question

Work within this document, and be sure to show all steps for arriving at your solution.

1) Consider the following sets (30 points):

U = {a, b, c, d, e, f, g}
A = {b, c, d, f}
B = {a, d, g}
C = {a, e}

Represent each of the following with an array of zeros and ones:

a) A ∩ B =

b) C ∪ B =

2) Consider the following two propositions (30 points):

p: It snows tonight.
q: I will stay home.

Use negation (~), conjunction (^), disjunction (?), and/or implication (→) to construct a logical equivalence of p→q.

Construct the truth table for both statements and explain how the truth tables establish logical equivalences.

P	Q	p→q
T	T
T	F
F	T
F	F

P	Q
T	T
T	F
F	T
F	F

3) Consider the statement "There does not exist a narwhal that can live on land." Write an equivalent English statement that begins with the words "Every narwhal.

Let P(x) be the predicate "x can live on land," where the variable x represents animals. Write both statements symbolically using P(x) and quantifiers, (∃, ∀).

4) Use Bacon's code to create a dummy message for BURDEN. For the sake of simplicity, use bold font for 0 and regular font for 1. (30 points)

5) At a regional competition, 7 male runners compete in a 100-meter sprint and 5 female runners compete in a separate 100-meter sprint. How many different arrangements are possible for a first-, second-, and third-place male runner and a first- and second-place female runner together?

6) How many distinguishable permutations can be made of the letters in the word AMERICA?

Answer 1

For the following statistics and probability question, provide answer to all the questions illustrated below by showing the whole computation part. Q1. At regional competition, 7 male runners compete in a 100-meter sprint and 5 female runners compete in the separate 100-meter sprint. Determine how many various arrangements are possible for a first, second and third-place male runner and the first and second place female runner altogether? Q2. Determine how many distinguishable permutations can be made of the letters in the word AMERICA? Q3. Make use of Bacon's code to make a dummy message for BURDEN. For sake of ease, use bold font for 0 and regular font for 1. Q4. Consider the statement ‘There doesn’t exist a narwhal which can live on land’. Write down an equivalent English statement which starts by the words "Every narwhal. Let P(x) is the predicate ‘x can live on land’, in which the variable x symbolizes animals. Write both the statements symbolically.