Chapter 2

{ x | 10 < x < 20 }

(10, 20)

The cardinality of the set which contains every other letter in the English alphabet starting with A (e.g. A, C, E...) is

13

What is the resulting value of the following? S space equals space left curly bracket minus 1 comma space minus 2 comma space minus 3 comma space 4 right curly bracket sum for j element of S of j squared

30

What is the resulting value of the following? ∑from k space equals space 1 to 267 of k

35,778

What is the resulting value of the following? sum from k equals 37 to 123 of k

6(,)?960

A = 1 0 4 -1 3 5 -1 2 2 + 2 2 -3 0 -2 -3 2 -3 0 A space equals space open square brackets table row 1 0 4 row cell minus 1 end cell 2 2 row 0 cell minus 2 end cell cell minus 3 end cell end table close square brackets plus open square brackets table row cell minus 1 end cell 3 5 row 2 2 cell minus 3 end cell row 2 cell minus 3 end cell 0 end table close square brackets

A = 0 3 9 1 4 -1 2 -5 -3

Which law is being applied? A = {1,2,3} B = {2,3,4} C = A ∪ B = {1,2,3} ∪ {2,3,4} = {1,2,3,4} A ∩ C = {1,2,3 } ∩ {1,2,3,4} = {1,2,3}

Absorption Law

A = 2 0 2 3 1 -3 -1 0 0 Which of the following matrices, when multiplied with A, will equal its identity matrix? AB = 1 0 0 0 1 0 0 0 1

B = 0 0 -1 1.5 1 6 0.5 0 1

A = 0 1 1 0 B = 1 0 1 0 c = A ⊙ B

C = 1 0 1 1

A = 2 -1 0 5 2 -4 B = 8 -5 1 2 -5 0 C = AB

C = 15 -11 62 -21

A function is defined as having an input that may map to more than one output.

False

A set which contains the empty set is the same as the empty set.

False

What is the truth set of the following predicate where the domain is the set of integers? Q(x): x² > x

z - {0,1}

What is the following result? A={0,1} B={0,1} AxB

{(0, 0), (0, 1), (1, 0), (1, 1)}

What is the result of the following? A = {a, b, c} B = {x, y} C = {0, 1} C x A x B

{(0,a,x), (0,a,y), (0,b,x), (0,b,y), (0,c,x), (0,c,y), (1,a,x), (1,a,y), (1,b,x), (1,b,y), (1,c,x), (1,c,y)}

{ x ∈ Z | x² < 26 }

{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}

The terms on the right are part of a recurrence relation on the left. The first terms have been removed from the sequence if they appear in the relation. aₙ = aₙ₋₁ - aₙ₋₂, a₀ = -1

{..., -1, 0, 1, 1, 0}

Select all of the following that are countably infinite.

The integers that are multiples of 7. The integers greater than 10 The set of all C++ programs

The set A when intersected with the universal set results in itself.

True

{x | 10 ≤ x ≤ 30 }

[10, 30)

What are values of the following? ⌊1.1⌋ = [a] ⌊1.1⌋ = [b] ⌊-0.1⌋ = [c] ⌊-0.1⌋ = [d] ⌊½+⌈½⌉ ⌋ = [e]

[a] = 1 [b] = 2 [c] = -1 [d] = 0 [e] = 1

The terms on the right are part of a recurrence relation on the left. The first terms have been removed from the sequence if they appear in the relation. aₙ = naₙ₋₁ + a²ₙ₋₂, a₀ = -1, a₁ = 0

{..., 1, 3, 13, 74, 613, 9767}

The terms on the right are part of a recurrence relation on the left. The first terms have been removed from the sequence if they appear in the relation. aₙ = -2aₙ₋₁, a₀ = -1

{..., 2, -4, 8, -16, 32}

The terms on the right are part of a recurrence relation on the left. The first terms have been removed from the sequence if they appear in the relation. aₙ = aₙ₋₁ + aₙ₋₂ + aₙ₋₃,a₀ = 1, a₁ = 1, a₂ = 2

{..., 2, 1, 1, 2, 2}

The terms on the right are part of a recurrence relation on the left. The first terms have been removed from the sequence if they appear in the relation. aₙ = 3a²ₙ₋₁, a₀ = 1

{..., 3, 27, 2187, 13438907, 617673396283947}

{ x | x = 2k and k ∈ N }

{0, 2, 4, 6, 8, 10, ...}°

{ x | x is a positive integer less than 12 }

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}

{ x ∈ N | 1 ≤ 2x ≤6 }

{1, 2, 3}

(B ⊕ C) ⊕ A

{1,2,3,4,5,6,7,8}

A ∪ B

{1,3,4,5,6,7,9}

A ⊕ B

{1,4,6,9}

Match the left hand side with the right hand side. A - B

{1,9}

{ x ∈ Z⁺ | x > 10 and x ≤20 }

{11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

A - C

{1}

C ∪ B

{2,3,4,5,6,7,8,9}

B - A

{4,6}

(A - B) ∩ C

{9}

Match the left hand side bit strings with the right hand side sets given the following universal set. AA, U = {A, B, C, D, E, F, G, I, J, K, L, M, N, O, P, Q, R, S,T, U, V, W, X, Y, Z} 1111 0000 1111 0000 1111 0000 11

{A, B, C, D, I, J, K, L, Q, R, S, T, Y, Z}

Match the left hand side bit strings with the right hand side sets given the following universal set. U = {A, B, C, D, E, F, G, I, J, K, L, M, N, O, P, Q, R, S,T, U, V, W, X, Y, Z} 1100 1100 1100 1100 1100 1100 11

{A, B, E, F, I, J, M, N, Q, R, U, V, Y, Z}

Match the left hand side bit strings with the right hand side sets given the following universal set. AA, U = {A, B, C, D, E, F, G, I, J, K, L, M, N, O, P, Q, R, S,T, U, V, W, X, Y, Z} 1010 1010 1010 1010 1010 1010 10

{A, C, E, G, I, K, M, O, Q, S, U, W, Y}

{ x | x is a letter of the word ALUMINIUM }

{A, I, M, L, N, U}

{ x | x s the first letter of every month }

{J, F, M, A, S, O, N, D}

Match the left hand side bit strings with the right hand side sets given the following universal set. U = {A, B, C, D, E, F, G, I, J, K, L, M, N, O, P, Q, R, S,T, U, V, W, X, Y, Z} 0000 0000 0000 1111 1111 1111 00

{M, N, O, P, Q, R, S,T, U, V, W, X}

(Select all that apply) Which of these statements is true?

{∅} ⊆ {∅} ∅ ⊂ {1} {∅}∈{{∅}}

(Select all that apply)Which of these statements is true?

{∅}∈{∅,{∅}} ∅∉ {0} {x} ∉ {x} {0} ∈ {{0}}

Given the following set what is its power set's cardinality? A = {1, 2, ∅}

|P(A)| = 8

What is the truth set of the following predicate where the domain is the set of integers? P(x): |x³| < 0

∅

{}

∅