Simplify ¬(s^(qv¬s)) to ¬sv¬q

Q: laws of logic to show that ((s VrV¬r) ^ (SV¬rva) ^ (rv¬sva)) = q v¬s.

A: The commutative law deals with the order of operations or the sequence in which elements are…

Q: Which of the following is logically equivalent to: [(￢p ∨ q)∧(￢p ∨q) ∧(￢p ∨r)]→[(p ∨￢q)∧(￢p ∨￢q)…

A: the answers for both mcqs is given below

Q: *p → q)^(¬q v q) is Contradiction) true false

A: True

Q: Question 3 (a) Show that [¬p v (p ^ q)] ^ ¬q → ¬(p v q) by using logical equivalence identities.

A:

Q: Find a denial (or the negation) for "(3!x)P(x)".

A: Find a denial (or the negation) for ” (!)P(x)".   We first look at the negation of a statement…

Q: ∀p∀q∀r((p≡T ∧q≡F ∧r≡T) →[(p∧¬q)⨁r≡T])   TRUE        FALSE   because:     The contrapositive:

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

Q: Derive the following using natural deduction. (a) PQFPVR QVR (b) P→ (Q → R), P V R, ¬Q → ¬P = R

A: Given,  1. P - ( Q - R )  2. P V R  3. Q - P  . R  4 . P - Q  5. P V R  6. P - ( Q - R )  7 . R…

Q: Simplify the following assertions (so that ¬ does not appear).

A: Answer to the above question is given below

Q: Simplify pA(-svs) to p 1. Select a law from the right to apply Laws Distributive Pa(-svs)…

A: NOTE   Below is the answer for the given question.   Hope you understand it well. If you have any…

Q: (¬P ∧ ¬R) ∨ (P ∧ ¬Q ∧ ¬R) is equivalent to ¬R ∧ (Q ⇒ ¬(P ∧ ¬R))

A: TO PROVE LHS = RHS THAT IS    -->  (¬P ∧ ¬R) ∨ (P ∧ ¬Q ∧ ¬R) is equivalent to ¬R ∧ (Q ⇒ ¬(P ∧…

Q: Transform the following into a DNF a) P → (Q → P)   b) (P ∨ Q) ∧ R

A: DNF or Disjunctive Normal Form is a type of normalization form of any logical expression. This form…

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: justify whether each of the following functions is injective, surjective, bijective, or none of…

A: following function is surjective

Q: Simplify (-mas)v¬(mvs) to -m 1. Select a law from the right to apply (¬mas)v¬(mvs)

A: We are given a logic expression which we are going to simplify using some inference laws which are…

Q: 6)For each of the following equivalences, determine if it is valid for all predicates P and Q. If…

A: Answer: We have given some equivalence relation and we need to check which is valid and which one is…

Q: Prove that the following wff is a tautology, a contradiction or neither. Be sure to say which one.…

A: Tautology: A tautology is a statement that is always true, no matter what the circumstance. It is a…

Q: Simplify m∨(¬s∧s) to m

A: Answer: Given expression is: m∨(¬s∧s) to m

Q: a) P→q^r q→ r d-:: b) bvd- ¬(pvr)→s r-p :.S

A: Here our task is to prove the given logical statements. Here we have given two questions, Each of…

Q: Prove that the following are logically equivalent: 1. qv~ (¬p A q) = r 2. (рАq) V (p А -9) 3D р

A:

Q: Is the following argument valid or not? I recommend an abbreviated table. -P(a) ^ (¬Q(b) v Q(c)),…

A: Correct Answer is Option ("D") i.e... It is invalid Explanation: It is a validity of a statement it…

Q: Conver the following to DNF and CNF form: (A ∨ B) → (C ∧ D)

A: Answer: DNF: ⇒(A∨B)→(C∧D)⇒τA∨B∨(C∧D)⇒A-∧B-∨(C∧D)

Q: Simplify the compound statement ¬(p ∧ (q ∨ r) ∧ ((p ∧ q) → r)).

A: In this question we have been given a compound statement and we need to simplify this statement.

Q: PA¬P = false Pv false = P -(-P) = P P → Q = ¬P V Q

A: There are total 4 expressions given. We have to find the value of P and Q variables. Expressions: P…

Q: Simplify ((true ∧ b ) ∨ ( b ∧ c ) ∨ ( true ∧ c )) ⊕ (( false ∧ b ) ∨ ( b ∧ c ) ∨ ( false ∧ c ))

A: In step 2, I have provided  ANSWER  with  brief  explanation------------

Q: (p + rר)= ((p + qר) →→ (p^q)) (qריר + ((pר \/ r V (r−))→

A: Answer : Logical Equivalence : 1) In order to declare the logical equivalence between any two…

Q: How to use rules of logic to simplify ¬q∧(p⇒q) ?

A: Given expression is, ¬q∧(p⇒q) It contains the variables p and q.

Q: Select the prope

A: A relation is said to be a function from a set A to a set B, if for each element of A, there exists…

Q: Write the following in disjunctive normal form using logical equivalences ( p ∨q) →(p ∧¬r).

A: A Disjunctive normal form is the way of expressing the expression as disjunction of conjunctions A…

Q: В - (В -А) = AnB (А -С) ) n (С -B) —Ф

A:

Q: Construct the truth (tables) values of the given compound proposition: [(p^q'Ar) + (p O q)] – [(p' &…

A: XOR is represented by ⊕. AND is represented by ∧. OR is represented by ∨. ↔ represents…

Q: (1) sin(5æ) = 5 sin(æ) – 20 sin (x) + 16 sin° (æ) - (2) sin? (x) cos² (æ) 1 – cos (4z) 8 a) Make an…

A:

Q: Find a closed form representation for the function defined recursively by f(0) = 5 and…

A: We have to find the solution of the given recurrence relation and prove the solution using induction…