Question

1. Prove p∧q=q∧p 2. Prove[((∀x)P(x))∧((∀x)Q(x))]→[(∀x)(P(x)∧Q(x))]. Remember to be strict in your treatment of quantifiers .3. Prove...

1. Prove p∧q=q∧p

2. Prove[((∀x)P(x))∧((∀x)Q(x))]→[(∀x)(P(x)∧Q(x))]. Remember to be strict in your treatment of quantifiers

.3. Prove R∪(S∩T) = (R∪S)∩(R∪T).

4.Consider the relation R={(x,y)∈R×R||x−y|≤1} on Z. Show that this relation is reflexive and symmetric but not transitive.

Homework Answers

Answer #1

1.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the relation R defined on the set R as follows: ∀x, y ∈ R, (x,...
Consider the relation R defined on the set R as follows: ∀x, y ∈ R, (x, y) ∈ R if and only if x + 2 > y. For example, (4, 3) is in R because 4 + 2 = 6, which is greater than 3. (a) Is the relation reflexive? Prove or disprove. (b) Is the relation symmetric? Prove or disprove. (c) Is the relation transitive? Prove or disprove. (d) Is it an equivalence relation? Explain.
Disprove: The following relation R on set Q is either reflexive, symmetric, or transitive. Let t...
Disprove: The following relation R on set Q is either reflexive, symmetric, or transitive. Let t and z be elements of Q. then t R z if and only if t = (z+1) * n for some integer n.
Let A = {1,2,3,4,5} and X = P(A) be its powerset. Define a binary relation on...
Let A = {1,2,3,4,5} and X = P(A) be its powerset. Define a binary relation on X by for any sets S, T ∈ X, S∼T if and only if S ⊆ T. (a) Is this relation reflexive? (b) Is this relation symmetric or antisymmetric? (c) Is this relation transitive?
Determine whether the relation R is reflexive, symmetric, antisymmetric, and/or transitive [4 Marks] 22 The relation...
Determine whether the relation R is reflexive, symmetric, antisymmetric, and/or transitive [4 Marks] 22 The relation R on Z where (?, ?) ∈ ? if ? = ? . The relation R on the set of all subsets of {1, 2, 3, 4} where SRT means S C T.
Consider the following relation on the set Z: xRy ? x2 + y is even. For...
Consider the following relation on the set Z: xRy ? x2 + y is even. For each question below, if your answer is "yes", then prove it, if your answer is "no", then show a counterexample. (i) Is R reflexive? (ii) Is R symmetric? (iii) Is R antisymmetric? (iv) Is R transitive? (v) Is R an equivalence relation? If it is, then describe the equivalence classes of R. How many equivalence classes are there?
Consider the relation R defined on the real line R, and defined as follows: x ∼...
Consider the relation R defined on the real line R, and defined as follows: x ∼ y if and only if the distance from the point x to the point y is less than 3. Study if this relation is reflexive, symmetric, and transitive. Which points are related to 2?
Complete the following table. If a property does not hold give an example to show why...
Complete the following table. If a property does not hold give an example to show why it does not hold. If it does hold, prove or explain why. Use correct symbolism. (Just Yes or No is incorrect) R = {(a,b) | a,b ∃ Z: : a + b-even S = {(a,b) | a,b ∃ Z: : a + b-odd T = {(a,b) | a,b ∃ Z: : a + 2b-even Relation Reflexive Symmetric Anti Symmetric Neither Symmetric or anti-symmetric Transitive...
Problem 3 For two relations R1 and R2 on a set A, we define the composition...
Problem 3 For two relations R1 and R2 on a set A, we define the composition of R2 after R1 as R2°R1 = { (x, z) ∈ A×A | (∃ y)( (x, y) ∈ R1 ∧ (y, z) ∈ R2 )} Recall that the inverse of a relation R, denoted R -1, on a set A is defined as: R -1 = { (x, y) ∈ A×A | (y, x) ∈ R)} Suppose R = { (1, 1), (1, 2),...
Determine whether the relation R on N is reflexive, symmetric, and/or transitive. Prove your answer. a)R...
Determine whether the relation R on N is reflexive, symmetric, and/or transitive. Prove your answer. a)R = {(x,y) : x,y ∈N,2|x,2|y}. b)R = {(x,y) : x,y ∈ A}. A = {1,2,3,4} c)R = {(x,y) : x,y ∈N,x is even ,y is odd }.
4. Prove that {(x, y) ∈ R 2 ∶ x − y ∈ Q} is an...
4. Prove that {(x, y) ∈ R 2 ∶ x − y ∈ Q} is an equivalence relation on the set of real numbers, where Q denotes the set of rational numbers.