1. (a) (b) (c) (d) Prove or disprove that, for any universal set U and predicates P and Q, [3r EU, P(x) ^ Q(x)] → [x = U, P(x)) ^ (3x = U, Q(x))] Prove or disprove that, for any universal set U and predicates P and Q, [3r EU, P(x)) ^ (3x U, Q(x))] → [r € U, P(x) ^ Q(x)] Prove or disprove that, for any universal set U and predicate P [3r € U, P(x)] → [Vr € U, P(x)] Prove or disprove that, for any universal set U and predicate P [Vr U, P(x)] → [3r € U, P(x)]

Q: 5) Let R be a binary relation over the positive integers defined as follows: R = {(a, b) | 2b < a <…

A: Since you posted a multi sub part question but according to guidelines we will solve first three sub…

Q: 4) Consider the equivalence claim: (Vx € R)(3! y E R)P(x,y) = (3! y € R)(Vx € R)P(x,y). (4.1) What…

A: Given equivalence claim is ∀x∈ℝ∃! y∈ℝPx,y≡∃! y∈ℝ∀x∈ℝPx,y The domain of a predicate is the set of all…

Q: Determine whether each of the following is a closed set. (a) A = [2,3] U [4,7] (b) B = (-∞, 2] U…

A: As per bartleby guidelines we do only first three subparts and rest part can be reposted separately.

Q: For each condition below, give an example of a set that satisfies that condition, or prove that one…

A: The given of the question is a list of conditions related to sets and subsets of real numbers, and…

Q: 10. Prove that for subsets X, Y, and Z of a given universal set U (a) X-Y=X-(XnY)= (XUY) - Y (b)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the infimum and supremum for the sets below. In some cases, the answer may be t∞. (a) A = {2n…

A: a  A=2n: n∈ℕ=21, 22,....InfimumA=2SupremumA=∞b B=-12n: n∈ℕ     B=-12,14,-18,116,....Infimum…

Q: A = { 3, 0, 1 } B = { y, x }  what is the cardinality of A x P(B) ?

A: Given that, A = {3,0,1}  B ={ y , x }  Power set of B = {{},{x},{y},{x,y}}  Generally cardinality is…

Q: Prove that (A ∪ B) − A = B − (A ∩ B) using: (a) the choose-an-element method (b) the algebra of set

A: We have to prove the set using two methods.

Q: 5. Prove that the following equivalences are tautology. Show your work in detail. For each step, you…

A: The equivalence relation is : The main aim is to prove that the equivalences are tautology.Tautology…

Q: 5. For each pair of sets, give an explicit bijection from one to the other, showing that they have…

A:

Q: (2) (a) Show using set identities that AUBU (AOBOT) = AUBUT (b) Prove by contradiction that if A C…

A:

Q: According to the Root Locus rules: O A) Root Locus starts at zeros the of G(s) and ends at the zeros…

A: The root locus is used to predict the behaviour of the closed-loop system.

Q: 6. Let 2 be a set and f, g: → R. Assume max{f(x) + g(x) | x = }, max{f(x) |x€N}, and max{g(x) | x =…

A:

Q: 1. (a) (b) (c) Prove or disprove that, for any universal set U and predicates P and Q, [x EU, P(x)…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Let P(x; y) : x plays in y A(x) : x is athletic. S(x) : x is smart.  E(y) : y is in English…

A:

Q: 1. (a) For a set A, P (A) is the set of subsets of A. Write down all the different elements of the…

A: Note: We are entitled to solve only the first question, unless specified 1) (a) We know the power…

Q: (1) In the universal set U ={1,2,3,4,5} we define the following sets: A ={1,2,3}, B = {3,4}, and C =…

A: Note: You have posted a question with multiple subparts. We have solved the first three subparts for…

Q: Justify rigorously the given set is open in R³. (a) A = {(x, y, z) |x>0, y 9}. (b) B = {(x, y, z) |…

A:

Q: For each of the following sets, decide whether it is finite, countable, or uncountable. Explain your…

A: Let  be any set , then

Q: 5) Let R be a binary relation over the positive integers defined as follows: R = {(a, b) | 2b < a <…

A:

Q: a. Which of the eight properties are satisfied by N? Give examples of the properties which are not…

A:

Q: A = {x € Z: xis even} {91'SI'ZI'6'S'E} = 5 23242+3 2184 21+ 122198 th

A: Given,            To find the value of

Q: prove or dis Prove a Every convex set of avectory is affine set- • Every affine set is sub space

A: A convex set is a subset of a vector space (such as Euclidean space) where for any two points within…

Q: State whether the propositions in parts (a) through (j) are TRUE or FALSE considering the following…

A: The given sets are X=a,1,a,a,a,1,∅, Y=a,3,a,1,a

Q: Let R ⊆ ℝ×ℝ with R={(x,y)|⌈x⌉=⌈y⌉}, that is, x and y round up to the same number. Characterize R in…

A: Given problem is :

Q: (a) |([10]² – {1,3} × {2, 5, 6}) — {5, 7, 9} × {8, 10}|.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 1) Let f: A ->B with C1 C C2C A and Dic D,CB Which is true? a) f(C) c f(C2) OR b) f(C2) c f(C:) (i)…

A: Given: i) To prove that answer is correct. ii) To give a counterexample to show that the set…

Q: 11. Show that the set of real numbers with the usual topology is not homeomorphic to the R set of…

A:

Q: Let X, Y and Z be subsets of the universal set U. Prove using ONLY definitions (logical connectives)…

A:

Q: 1. Let A = {−30, -10, 10, 30, 50} and B = {-20, -10,0, 10} be subsets of the universal set ε = {10x:…

A:

Q: 1. Two sets A and B as under: A = {(a, b) e Rx R:a-5 < 1 and b-5< 1}; B = {(a, b) e Rx R: 4(a-6) +…

A:

Q: An element x in R is called nilpotent if x = 0 for some m € 2¹. Let x be a nilpotent element of the…

A: An element x in R is called nilpotent if  for some .To Find:a) Prove that x is either zero or zero…

Q: 7. A binary relation * is defined by the following truth table y x * y F F T T T Which of the…

A: We can make a truth table by considering the options and find which is not equivalent.

Q: 1. If X~ B(15,0.45) find, A) P(X = 7) Multilevel List B) P(5 9)

A:

Q: · Let t:R>R?and ECIR be given by fixiiX=3+ X2 , X;-283) and by E={(X,X2,X+)ER:15Xf+x?+XZ Decide It…

A: