For all sets A, B, and C, it holds that (An C) U (B \ C) = (B U C) \ (C \ A).
Q: Let S be a set of n lines in the plane such that no two are parallel and no three meet in the same…
A: Let S be a set of n lines in a plane such that notwo are parallel and no three meet in the same…
Q: f(x) is O(g(x)) if and only if g(x) is Ω(f(x)).
A: Proof: given: f:R---->R g:R----->R f(x) is O(g(x)) so we can say |f(x)|≤c|g(x)|.........(1)…
Q: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} are two sets. find R = {(x, y): x e X and y e Y and (y –…
A: Given Data:- X = {1,2,3,4,5} Y = {7,11,13} To Find:- Relation R such that R = { (x,y) : x∈X and…
Q: Prove that A → B E (Vx)A → (Vy)B, if y is not free in B.
A:
Q: Let A, B be any two sets. Prove that if A S B, then A n B = p.
A:
Q: Find the sets A and B if A - B = {1, 5, 7, 8}, B - A = {2, 10}, and A NB= {3, 6, 9}.
A: let us see the answer:-
Q: Give an explicit formula for a function from the set of all integers to the set of positive integers…
A: given: explicit formula for a function from the set of all integers tothe set of positive integers…
Q: Let U = {1,2, 3, 4, ..., 10}, A = {2,4, 6}, B = {6,7,9}, and C = {6,9} %3D %3| a. Let X = (B - A) U…
A:
Q: Describe each of the following sets.
A: R means real number : all number except complex numbers, means R=…
Q: a) Let O be the set of odd numbers and O' = {1, 5, 9, 13, 17, ...} be its subset. Define the…
A:
Q: Show by membership that for all sets A, B and C: A – (AnB) CA – B
A: We've done so. A−(A∩B) =A∩(A∩B)c [ Because we have XY=XYc for any two non-empty sets X and Y, where…
Q: 3) Show that the set of three-dimensional coordinates {(r,y, z)|x, y, z E Z} has size equal to N.
A: N stands for Natural numbers in number system.
Q: 5. Simplify the following functions using a K-map: e)F(X,Y,Z)=X'Y'Z'+X'YZ+XY'Z+XYZ
A: F(X,Y,Z) = X'Y'Z' + X'YZ + XY'Z + XYZ where, No. of variables is 3 i.e. x, y, z
Q: ;Let E be a set of alphabets and let A and B be subsets of 'with ACB. Prove that A C B*.
A: It is given that Σ is a set. Now what is Σ* ? Σ*= set of all possible strings made from elements of…
Q: Let A be the set {1,3,5,7,9} and B be the set {1,2,4,8} . Find the integer value |AxB|
A:
Q: Show by membership that for all sets A, B and C: A - (AnB) CA-B
A: We are given a relation in sets and we have to prove whether given relation is true or not. We will…
Q: Show by membership that for all sets A, B and C: А - (AnB) CA - В
A: Given: We have to show that for all sets A , B and C: A - (A ∩ B) ⊆ A - B
Q: Let L be a strict subset of LAc (i.e. L c LACC). Then L is ( always / sometimes / never ) decidable.
A: Defined the given statement always, sometimes or never
Q: Prove by contradiction, for any sets A and B , if A C A– B, then An B=Ø
A: Here given, two sets A and B; given: A ⊆ A-B To prove:A∩ B=∅
Q: The Boolean expression F(A,B,C,D) = E(0, 3, 4, 7, 10, 12) is simplified using: Select one: O a. 2-V…
A: F(A,B,C,D)=SIGMA(0,3,4,7,10,12) is simplified using 4 variable K-map. Option c.4-V K map is answer
Q: Let A be the set {1,3,5,7,9} and B be the set {1,2,4,8} . Find the integer value |(AxB) ꓵ (BxA)|
A: - We need to highlight the value |(AxB) ꓵ (BxA)| Where, A = {1,3,5,7,9} B = {1,2,4,8}
Q: 5. Show that for every partially computable function f(x,,..., x,), there is a number m 2 0 such…
A: Answer: I have given answered in the handwritten format
Q: Determine the cardinality of the power set of S, show the formula used to do so. Show the power set…
A: Power set of any set is obtained by forming the set of all subsets. Thus, for every element we have…
Q: {[ {[::]-« 0 0 a (b): Let U = : a, b E R} and W: : c, d ER} be 0 0 two subspaces of M2 (R). Show…
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Q: . Let Q, R and S be sets. Show that (R – Q) ∪ (S – Q) = (R ∪ S) – Q.
A: Given: Let Q, R and S be sets. Show that (R – Q) ∪ (S – Q) = (R ∪ S) – Q.
Q: Is A a subset of B if; A = { 9, 8, 7, 6, 5} B ={ 5,6, 7, 8, 9}
A: Overview : A collection of elements is known as a subset if all the elements of the set are…
Q: Prove that for all sets A, B, and C, (A∩B)−C = (A−C)∩B
A: We have 3 sets A, B, C. We need to prove that - (A∩B)-C = (A-C)∩B
Q: Use the pumping lemma to prove that the following language is not context-free. Show all cases on…
A: Pumping lemma for CFL is used to prove the language is not cfl using some valid string s. Never use…
Q: Prove that x, where y is the domain of all real numbers, if x²(y² - 2y) is odd, then x and y are
A: A function f is termed as odd if the condition f (-x) = -f (x) holds. Whereas a number is odd if it…
Q: . Find x if 8, x, 7, 6, 6, 5, 4, 3, 3, 1, 1, 1 is graphical.
A: Applying Havel–Hakimi Theorem : Consider x = 8 8, 8, 7, 6, 6, 5, 4, 3, 3, 1, 1, 1 Subtracting 1…
Q: 3. If a and b are any two positive naturals, then the set {a + bi: i is a natural} contains…
A: Set a+bi cannot have infinitely many prime numbers.
Q: Let A = {1,2,3,..., 10}. Consider the function f : P(A) → N given by f(B) = |B|. That is, f takes a…
A: The co-domain or range of f are the possible values of cardinality of the input set, which can go…
Q: Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) =…
A: EXPLANATION: Composition of function is basically the application of one kind of function to the…
Q: (C - B) n (Ã U B) (A U B) – (A n C) (A - B) U (A - C)
A:
Q: Is A a subset of B if; A = {5,2,1} B ={ 6, 1, 2
A: In mathematical computation, a set X is considered to be a subset of another set Y if X consists of…
Q: (1) (a) For any sets A, B, and C. Show that (AUBUC)U(A – (BUC)) = BUC |
A: The answer is given in step 2.
Q: Discrete Math Let A, B, and C be finite sets with |A| = 6 |B| = 8 |C| = 6 |A ⋂ B| = 3 |A ⋂ C| = 2…
A: Prove thatP(A ∪ B ∪ C) = P(A) + P(B) + P(C) − P(A ∩ B) − P(A ∩ C) − P(B ∩ C) + P(A ∩ B ∩…
Q: Let X = {1, 2, 3, 4, 5} and Y = {7, 11, 13} are two sets. find R = {(x, y):xEX and y EY and (y - x)…
A: Given: X={1,2,3,4,5} Y={7,11,13} find R={(x,y):x∈X and y∈Y and(y-x) is divisible by 6}
Q: Given the sets A={1,2,a,d,f} and B={a,b,c,d,e,f}. The cardinality of A – B is
A: Here in this question we have two set A and B A={ 1 ,2 ,a , d, f} B={ a, b, c, d, e, f} We have to…
Q: Let f be a function from the set of length 10 binary numbers to the set of subsets of A={1, 2,…
A: Let f be a function from set A to set B. If f is a one-to-one correspondence( one-to-one, and onto),…
Q: Give an explicit formula for a function from the set of integers to the set of positive integers…
A: A function f from A to B has the property that each element of A has been assigned to exactly one…
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- Let the universal set be the set ? of all real numbers and let ? = {x ∈ r |0 < x ≤ 2},? = {x ∈ r |1 ≤ x < 4}, ? = {x ∈ R |3 ≤ x < 9}. 4 what is A U CGiven the sets A = { A, B, C, D} and B = {C, D, E}, what is A v B A-BLet the universal set be the set ? of all real numbers and let ? = {x ∈ r |0 < x ≤ 2},? = {x ∈ r |1 ≤ x < 4}, ? = {x ∈ R |3 ≤ x < 9}. 3 what is Ac
- For each of the following subsets of {0, 1}∗ tell whether or not it is regular. Proveyour answer.(a) {x | #1(x) = 2.#0(x)}(b) {x | #1(x) − #0(x) < 10}(c) {x | #1(x).#0(x) is even}Suppose we have the following sets: P, Q, and R. Prove or disprove that if for all x, (x ∈ P) → ((x ∈ Q) → (x ∈ R)), then P ⋂ Q ⊆ RComputer Science Let a M be a finite set of messages, and let S(M) denote the set of all permutations of M (all bijective functions f : M → M). We’ll assume that if given a description of σ ∈ S(M), both σ and σ −1 are efficiently computable. Suppose P ⊂ S(M) is such that ∀x, y ∈ M, ∃σ ∈ P such that σ(x) = y. (a) Show that |P| ≥ |M|. (This is easy, but makes sure you’ve parsed the definition.) (b) Show that if |P| = |M|, then the following encryption scheme is perfectly secure, provided you only use it once: 1 Key generation: select a random σ ∈ P; Encryption: m 7→ σ(m) Decryption: c 7→ σ −1 (c) (c) Show that the above is false if |M| < |P| < 2|M|. (d) Observe that for any finite group G and any g ∈ G, the map x 7→ gx is a permutation of G. By viewing G itself as a set of permutations of G in this way, show that the above property is satisfied (with M = P = G). (e) The traditional xor one time pad is a special case of the above. What is the finite group in this case?
- We consider certain strings of length 6 over the alphabet S = {A,B,C}. We require that the string contains exactly two As, and exactly two B's, and exactly two C's. How many such strings are there? That is, how many strings of length 6 over the alphabet {A,B,C} contains exactly two A's, two B's and two C's?Let Σ = {a, b}. Indicate whether or not L is regular and prove your answer. (i) L={w ∈ {a, b}* : w contains at least two a’s and at most three b’s}. (ii) L={a^ib^j : i, j ≥ 0 and i < j.}.5. Let R = {1, 3, π, 4, 1, 9, 10}, S = {{1}, 3, 9, 10}, T = {1, 3, π}, and U = {{1, 3, π}, 1}. Which of thefollowing are true? For those that are not, why not? (d) 1 ⊆ U(e) {1} ⊆ T(f) {1} ⊆ S(g) {1} ∈ S