Given the set F = {A→B, AB→C, AC→BD} of functional dependencies, prove the following dependencies by using the Armstrong axioms. A -> ABC AD -> BCD

Q: 2. Prove the following in SDE. A V B, A → C, B →→C - C

A:

Q: Convert the following CFG to an equivalent CFG in Chomsky normal form. Show all your work step by…

A: Here, we are going to convert the CFG into CNF. CNF stands for Chomsky Normal Form. CNF rules are:…

Q: recurrence relation

A: Given :- In the above question, the recurrence relation along with the initial values is mention in…

Q: compute in polynomial is P(x) =x° +x* +x²+x + 1. Given A(x) = x+x*+x°+x, find A'(x) mod P(x)

A: Given  The answer is given below.

Q: 37. Construct a truth table for each of these compound sitions. a) p→ (-q Vr) b) ¬p → (q→ r) c) (p…

A: First lets understand how each operator works: ∧ : And operator: p∧q : is true when both p and q are…

Q: Find the solution of recurrence relation of a =5a-1-6a2+3n+2" with initial condition a, = 0,a, = 1,…

A: Below I am adding solution for given recurrence relation

Q: Let G=(viE) be a diagrach, and E hie)3 ch,e)s. what is the mmber Of strongly connec tes Components…

A: Strongly connected component means: it is maximally connected subgraph where there is path from…

Q: Consider F = A → G, AG → DE, E → H, EC → B, A → D, determine (a) if AC → H can be inferred from F…

A: Given functional dependencies We have to find if AC->H can be inferred from FD or not.

Q: In recurrence relation T(n) = 2T(n / 3) + (1) the number of sub-problem are

A: Option (D) is the correct option.

Q: give the CFG of {y ∈ {0, 1}∗ | #0(y) ≤ 2#1(y)}

A: Let's see the solution in the next steps

Q: (A→¬C)→((B→¬D)→(A∨B→¬(C∧D))).

A: I have given an answer in step 2.

Q: Show that the CFG with productions S → a | Sa | bSS | SSb | SbS is ambiguous

A: Here in this question we have asked to show that the Grammer is ambiguous. S → a | Sa | bSS | SSb |…

Q: Construct CFG from the following productions of CFG S - aSbb | abb. Use the CFG method properly and…

A: Context Free Grammar: A grammar contain a context free grammar then it must be a context free…

Q: +}, ymmetric, whether it is antisymmetric, and whether it is transitive

A: a) relation R is not reflexive: (1,1),(4,4)\notin R(1,1),(4,4)∉R relation R is not symmetric:…

Q: et �=[5914], �=[−5−3−5], and �=[558] Are �,� and � linearly dependent, or are they linearly…

A: In this question we have to understand the linearly dependency of a linear relation.  Let's…

Q: Let f : B 3 → B where f(x, y, z) = (x + z)y. (a) Provide a truth table for the function. (b) Derive…

A: In Boolean algebra, the canonical disjunctive normal form (DNF) and canonical conjunctive normal…

Q: ) Find a BCNF decomposition of PLANET with work shown

A: A FD X->Y is said to be in BCNF when X is key for the given relation. Here primary key is (N)…

Q: ) [*+ Let R= {(1,2), (1,4), (2,3), (3,1), (4,2)} be a relation on {1,2,3,4}. Find the symmetric and…

A: The symmetric closure of a relation R on a set A is defined as the smallest symmetric relation on A…

Q: Convert the following CFG into Chomsky and Greibach Normal Forms: G=(N,T, P, E) N = {A, B} T = {x,…

A: Context-Free Grammars (CFGs) are used to describe the syntax of formal languages in computer science…

Q: 3. Which ene of the following comectly determines the solution of the recarence relation with…

A: Defined the given recurrence relation using master theorem

Q: 1. Prove the following equivalency relation: ¬P ∨¬Q≡¬(P ∧Q) 2. Prove the following equivalency…

A: Proving given equivalency relations using Truth tables: operators used: Not:~ ~P is true if P is…

Q: Show that (p → q)^ (p → r)is a Contingency.

A: I have provided solution in step2.

Q: .Solve please..

A: I have solved below:

Q: Remove Null productions from the given CFG S→bS | aA A→ bA   aF Λ F→ bF | Λ

A: NULL PRODUCTIONS: These are the productions of type S -> ℷ. A variable is said to be nullable if…

Q: P→Q, Q→¬P, PR, R∨¬Q use truth table to see if consisent

A:

Q: Draw the truth table of A→ (B→C) and (A →B) → C. Determine from the truth table whether A→ (B→C) is…

A: A B C (B→C) A→(B→C) T T T T T T T F F F T F T T T T F F T T F T T T T F T F F T F…

Q: Show that each of the following implications is a tautology by using a series of logical…

A: 1. 2. ~(p → q) → ~q3. ~p → (p → q) 4.  [p Ʌ (p → q)] → q Show that each of the following…

Q: Show that (p →q)^(p → r) and t using method of Proof

A: Solution - In the given question, we have to show that the two given propositions are logically…

Q: 2. Use Armstrong's axioms to prove the union rule: If a → B and a → y, then a → By.

A: Armstrong's Axioms are a set of rules of axioms.

Q: Give a recurrence relation for each of the following sequences: a. 8, -4,2,-1,,... b. 2,3,1,1,0,...

A: a. an+1​=−21​.an​b. an+1​=an​−21​Explanation:Solution a : To find a recurrence relation for the…

Q: the following proposition, describe (i) a model on which it is true, and (ii) a model on which it is…

A: Given For the following proposition, describe (i) a model on which it is true, and (ii) a model on…

Q: Show that a CFG G with productions S SS | (S) |A is ambiguous.

A: CFG G => S -> SS | (S) | A We have to prove that this grammar is ambiguous.   Condition for a…

Q: Show that every Deterministic CFG is an unambiguous CFG

A: DCFG:- A deterministic context-free grammar (DCFG) is a context-free grammar such that every valid…

Q: A = {1,3,7,9,10} , and let R be the relation on A defined by x < y', {(x, y) e A:x² < y} Write R as…

A: Here in this question we have given a set A{ 1,3,7,9,10} and a relation is defined as x^2 &lt;= y.…

Q: Use Armstrong’s axioms to prove the soundness of the union rule. (Hint: Use the augmentation rule to…

A: Armstrong's Rules in RDBMS:  William W. Armstrong stated two sets of rules for implementing…

Q: Consider the wff (p→q) → r. (2) (2a) Write down its contrapositive. (2b) Start with the…

A: Contrapositive: The contrapositive of a conditional statement is formed by negating both the…

Q: Describe in words the language of the following CFG, then give a CFG for its complement which you…

A: Solution:  In Formal Language, a CFL is a language generated by some CFG.The set of all CFL is…

Q: Define NFA. With example explain the extended transition functione

A: NFA: NFA stands for non-deterministic finite automata. A NFA consists of: A finite set of states S.…

Q: Use Tableaux algorithm to verify, whether formula (A→B)∧(A→(B→C))→(A→C) is derivable in classical…

A: Summary: The Tableaux Method replaces the statements "X is true" and "X is false" with their…

Q: Prove that the following CFG is ambiguous:

A: A Grammar is said to be ambiguous if it can generate a string in more than one way.  That is it can…