Simplify using conditional - disjunction equivalence (Example 3,Pg 28). (pnq) →p

Q: Show that the following language is decidable: L = {F | F is a boolean formula and F has 5…

A: A language is decidable if am alogorithm exits to define it. Existence of algorithm implies, that we…

Q: if p and q are logical variables, which of the following is a tautology (i.e., always correct…

A: p and q are logical variables here. There are total 4 boolean expressions given and we have to find…

Q: draw a Deterministic Finite Automaton (DFA) for the regular expression below, and make sure to mark…

A: The nodes in the DFA that indicate its current states are pink.

Q: Use the Pumping Lemma to prove that the language L= (a"b2n: n >= 0} is NOT context free.

A:

Q: Let L be the language {zzk : z belongs to E*}. Use the Pumping Lemma to show that L is not regular,…

A: Input Language : L = {zzk : z belongs to {m,n}* ,  k is any integer} Expanding Language : Using…

Q: :Q×(EU{2})→ P(Q)) respectively, where E={a,b}. а, b a a,b a,b b a

A: 1)  Let the final state be called q2 and other remaining state be q1.  Therefore the transition…

Q: Using truth table, prove the following tautologies a.a ⋀ (b ⋁ c) = a ⋀ b ⋁ a ⋀ c b.¬(a ⋀ c) = ¬a ⋁…

A:

Q: 1. Given L₁ = {a, abc, a c) and L₂ = {ab, c ba) are the languages over = {a, b, c), determine L₁ L2…

A: Given :

Q: Conjunctive Normal Form (CNF) for (P → (Q → R)) → (P → (R → Q)) is: ¬(¬P ∨ Q) ∨ (¬(¬Q ∨ R) ∨ (¬P ∨…

A: (P → (Q → R)) → (P → (R → Q)) is: X→Y⇒¬×VY(P → (Q → R)) → (P → (R → Q))⇒¬(P → (Q → R)) ∨  (P → (R →…

Q: Show that ¬(p → q) → ¬q is a tautology using rules (not a truth table

A: The given expression is a tautology. I am proving by rules. Please find hand written submission in…

Q: Problem 3. lence laws taught in the course. Prove the following equivalences using the equiva- 1.…

A: Answer: We have proof of the equivalence  with the help of Truth table and we have explain in each…

Q: Use the Laws of Equivalence  State clearly which law(s) you are using in each step. (a)  R → (¬Q →…

A: In this we only use one property that is P -> q is ¬p V q

Q: Example: Proof using Logical Equivalence ( p → r ) ˅ ( q → r ) ≡ ( p ˄ q ) → r

A: Given:  Proof using Logical Equivalence ( p → r ) ˅ ( q → r ) ≡ ( p ˄ q ) → r

Q: (p → (q v r)) → ((p ^ ¬q) → r) is O Contingency O Tautology O None of the choices O Contradiction O…

A: understanding some basic terms  1) tautology - a tautology is a proposition that is always true  2)…

Q: Q2 "Simplify the regular expression a:= (x'y)* + (x*(yx*)z)*(x*y)*xx* + € defined over the alphabet…

A: Answer (2) :  Regular expressions are patterns used to match character combinations in strings

Q: (a) Given a conditional statement r → p, find the inverse of its converse, and the inverse of it…

A: Conditional statements are a fundamental concept in logic and mathematics, commonly used to express…

Q: Prove the following equalities using equivalence laws: a. ¬(¬rA s) ^ (r V s) =r b. r→(-s→t) =…

A: Let's understand step by step :   Proving : Answer (a) : Given : ¬(¬r∧s) ∧  (r∨s) ≡ r   Now…

Q: 4. Convert the regular expression a(a|b)*a(a |ab) over Σ-fa, b into its equivalent DFA using Direct…

A: Regular expression to DFA

Q: EXERCISE 5.3 Verify whether (a → b) → b is a tautology. Is the following proof correct? If not, what…

A: A tautology is a formula that is always true, regardless of the truth values of its propositional…

Q: Give an dfa that accepts the language L ((a + b)∗b (a + bb)∗).

A: The DFA for the given language L ((a + b)∗b (a + bb)∗) is shown below:

Q: Using a truth table show that -(pq) → p is a tautology. Show all intermediate steps. Be sure to…

A: The following is the equivalent simplified expression for the "implies" expression: p q ~p q In…

Q: What is (a --> b) and (¬b --> c) and (¬ c↔¬b) logically equivalent to? Use logic laws and label them

A: Solution:   In order to solve this question, first let's understand the neede truth table.

Q: 29. p → (q \ r) = (p ^~q) → r

A: The question asks to use the biconditional (↔) operator to convert the logical equivalence P ->…

Q: Use the pumping lemma to prove that the language L over {a,b,c}", given by L = {wcv: |wa = |vl6} is…

A: First lets see Pumping lemma for regular languages: If a language L is regular, then there exist an…

Q: d) v d-) + bAd) v d-) (p v q, one of the followi either S, nor S, is IS

A: Solution - In the given question, we have to find whether S1 or S2 is a tautology or not.

Q: Th Conjunctive Normal Form (CNF) for (A → B) ∨ (B → A) is: (¬A ∨ B) ∨ (¬B ∨ A)

A: The Conjunctive normal form of  X -> Y => ¬X ∨ Y   Thus using this formula, we need to expand…

Q: Question 7: Prove the non-regularity of the given language L using pumping lemma. L={a"b?na2n}

A: Pumping lemma: Pumping lemma is used to prove non regularity of the language. The regular language…

Q: Prove the following logical implication (A ⇒ B) ⇒ ((C ⇒ A) ⇒ (C ⇒ B)) without a truth table

A: Answer in next step

Q: Prove the language L = {ww | w ∈ {x,y}∗} is non-regular. Explain each step of your reasoning with…

A: L = {ww | w ∈ {x,y}∗} is non regular is proved in step 2.

Q: Let p and q be two propositions. Consider the following two statements in prepositional logic.…

A: Here, two statements are given, S₁: (-p^(pv q)) → p S₂: q→(-p^ (pvq)) p and q are two propositions.…

Q: Prove that the following language is not context-free using pumping lemma: {xmy"xm| m >n + 1 > 0}…

A: Pumping Lemma for CFL states that for any Context Free Language L, it is possible to find two…

Q: Complete the truth table for the following compound statement. (p→q)↔(q→p)(p→q)↔(q→p) p q…

A: Mathematicians typically employ a binary logic, where each proposition can only take on one of two…

Q: Prove the predicate logic statement is valid: (∀ x)(P(x)) ∧ (∀ x)(Q(x)) → P(a) ∧ Q(b)

A: Introduction Predicate Logic: In mathematics and computer science, predicate logic is a formal…

Q: natural deduction

A: Given :- The logical expression or statements is mention in the above given question   Need to proof…