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

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: 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: 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: (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: 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: 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: 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: 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 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: 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…