Let A = {1, 2, 3}. For each of the following relations state (no proofs required)...

Let A = {1, 2, 3}. For each of the following relations state (no proofs required) whether it is (i) both a function and an equivalence relation (ii) a function but not an equivalence relation (iii) an equivalence relation but not a function (iv) neither a function nor an equivalence relation (a) {(1, 1),(2, 2),(3, 3)} ⊆ A × A (b) {(1, 1),(2, 2)} ⊆ A × A (c) {(1, 1),(2, 2),(3, 2)} ⊆ A × A (d) {(1, 1),(2, 2),(2, 3)} ⊆ A × A (e) {(1, 1),(2, 2),(3, 3),(1, 3),(3, 1)} ⊆ A × A

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

For each of these relations on the set {1, 2, 3, 4}, decide whether it is...

For each of these relations on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive. {(2, 4), (4, 2)} {(1, 2), (2, 3), (3, 4)} {(1, 1), (2, 2), (3, 3), (4, 4)} {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} For a) and b) please use the graph representation to determine their properties For c) and d) please use matrix...

Let ? = {?1, ?2, ?3, … … … … ?? } ?? ? = {?1,...

Let ? = {?1, ?2, ?3, … … … … ?? } ?? ? = {?1, ?2, ?3, … … … … ?? } Prove by induction that the number of injective functions ? from ? ?? ? is ?!

Let x3 be the following vector: x3 <- c(0, 1, 1, 2, 2, 2, 3, 3,...

Let x3 be the following vector: x3 <- c(0, 1, 1, 2, 2, 2, 3, 3, 4) Imagine what a histogram of x3 would look like. Assume that the histogram has a bin width of 1. How many bars will the histogram have? Where will they appear? How high will each be? When you are done, plot a histogram of x3 with bin width = 1, and see if you are right. I need code help R programming

3. For each of the following relations on the set Z of integers, determine if it...

3. For each of the following relations on the set Z of integers, determine if it is reflexive, symmetric, antisymmetric, or transitive. On the basis of these properties, state whether or not it is an equivalence relation or a partial order. (a) R = {(a, b) ∈ Z 2 ∶ a 2 = b 2 }. (b) S = {(a, b) ∈ Z 2 ∶ ∣a − b∣ ≤ 1}.

Let C be the following matrix: C=( 1 2 3 -2 0 1 1 -2 -1...

Let C be the following matrix: C=( 1 2 3 -2 0 1 1 -2 -1 3 2 -8 -1 -2 -3 2 ) Give a basis for the row space of Cin the format [1,2,3],[3,4,5], for example.

Let A = {1,2,3}. Determine all the equivalence relations R on A. For each of these,...

Let A = {1,2,3}. Determine all the equivalence relations R on A. For each of these, list all ordered pairs in the relation.

For each of the following three (3) scenarios, state two (2) violation of the Rules of...

For each of the following three (3) scenarios, state two (2) violation of the Rules of Professional Conduct: a) Bill Williams, CPA, began a telephone campaign to grow his client base. He began calling companies listed in the telephone directly within twenty (20) kilometres advising them of his accounting services. After making several phone calls, Bill finally landed a new audit client, Big Bob Autos. In order to secure this new business, Bill entered into an agreement with Bob whereby...

State the audit opinion that is required in each of the following circumstances and levels of...

State the audit opinion that is required in each of the following circumstances and levels of materiality: (i) Circumstance: The auditor is unable to obtain sufficient appropriate evidence concerning sales and inventory levels. Level of materiality: Material and pervasive. (ii) Circumstance: The auditor and management disagree about the application of accounting policies. Level of materiality: Material and pervasive. (iii) Circumstance: The auditor and management disagree about a disclosure. Level of materiality: Material but not pervasive (iv) Circumstance: The auditor is...

Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]. Let...

Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]. Let ?? be the ?-th smallest among {?1, ?2, ?3}. Find the variance of ?2, and the covariance between the median ?2 and the sample mean ? = 1 3 (?1 + ?2 + ?3).

PROOFS: 1. State the prove The Density Theorem for Rational Numbers 2. Prove that irrational numbers are dense in the set of real numbers

PROOFS: 1. State the prove The Density Theorem for Rational Numbers 2. Prove that irrational numbers are dense in the set of real numbers 3. Prove that rational numbers are countable 4. Prove that real numbers are uncountable 5. Prove that square root of 2 is irrational

Subjects