1. Prove the following entailment in SD. PQ, P →REP→ (Q ^ R)

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

A:

Q: Construct a truth table for (p--->(q--->r)) ---> ((p^q) V r)

A: A truth table is a mathematical tool used in logic to systematically evaluate the truth values of a…

Q: Write the ô function of the following (1) dfa (º DFA:QX2→Q) and (2) nf SNFA:Q×(EU{1})→P(Q) )…

A: DFA : DFA stands for deterministic finite automata. This machine (DFA) reads an input string one…

Q: Prove that (p →(q →r)) → ((p →q) →(p →r)) ≡ T for all propositions p, q, r.

A: A tautology is a logical statement that is true for all possible truth values of its propositional…

Q: Simplify the given POS function (a) k-mapping and (b) tabular method. Show your complete solution.…

A: F(A,B,C,D,E)=(0,2,4,5, 7, 8, 10, 12, 16, 18, 20, 23, 24, 25, 26, 27, 28)  Five variable K map.

Q: For f(a, b, c, d) = [] M (0, 1, 6, 8, 11, 12) • [[ D(3, 7, 14, 15), using a 4-variable K-Map find;…

A: We are given a 4 variable function in maxterms form.We are asked minimum Sum-of-products and…

Q: Prove the following statement (ab^bc) → ac

A: Given, (a|b ∧ b|c) -> a|c It can be represented as a ∨ b b ∨ c _____________ a ∨ c

Q: Complete the axiomatization by using and add a rule of universal generalization a) Ay/x) Vx…

A:

Q: LREJECT = {((M),1) : M rejects z} (a) Show that LREJECT iS recognizable (b) Show that TKJECT İS…

A:

Q: Solve this proof with no premises: (~Q->~P)->((~Q->P)->Q)

A: The objective of the question is to solve a logical proof with no premises. The proof is:…

Q: (A→¬C)→((B→¬D)→(A∨B→¬(C∧D))).

A: I have given an answer in step 2.

Q: 4. Show that -p → (p → q) is a tautology by using truth table.

A: Here in this question we have given an expression and we have asked to show that this is tautology.

Q: SCongider the Funcbion: F (Waya) =L(57,12,15) with don's care condition id (w,xy%.3) ={ (4,6,13,14…

A: Minimization of function is in step 2.

Q: Use algorithm TautologyTest to prove that the following expressions are tautologies. [ВЛ(4— B)] — b.…

A: Tautology means the expression which always true for all possible set of values.

Q: Show that (p ∧ q) ∨ ( p ∧ q) ≡ p using rules.

A: To show that (p ∧ q) ∨ ( p ∧ q) ≡ p using rules. Let us write ^ as '*' sign and other sign as '+'.…

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: 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: 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: 5)Prove that CNOT|x>ly> = |x> |x op y>, where op is an exclusive OR operator and CNOT is the…

A: The task is to prove that CNOT|x>|y> = |x> |x op y> for the controlled-not (CNOT) gate,…

Q: 3. Show that the identity sin²(x) a) x = 1-cos(2x) 2 holds for the following values of x. S b) x =…

A: Below is the answer:

Q: 4. Prove that ALLCFG Sm EQCFG-

A: 1. By contradiction. Assume that we have a decider R for EQCFG.2. Using R we construct a decider S…

Q: Using the pumping lemma, show {a^n b^m a^m b^n} is nonregular language. Show it by listing all…

A: To show that the language L = {a^n b^m a^m b^n | n, m ≥ 0} is not regular, we will use the pumping…

Q: 3. Prove the following theorem in SDE. (Q ^ -Q) → R

A: Given prepositional logic is  (Q∧¬Q)→R  Here is the two variables Q,R

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: A = {[(¬P → Q) AR] V ¬Q} → (QAR)

A: Answer: Answer is given in step 2

Q: 1. Prove the following entailment in SD. P→Q,P R E P→(Q ^ R)

A: The premises we have are P -> Q P -> R The conclusion is P -> (Q^R)  Here let's take P as…

Q: 5. Prove the following entailment in SD. A M, M→ (Q A K), A ► K VL

A: The solution fro the above given question is given below:

Q: Use truth table to prove the equivalence of following (pvq) → r= (pr) ^ (q→r)

A: A truth table is a representation of mathematical table in which all possible outcomes would occur…

Q: 3. Show that the identity sin²(x) = 1-cos(2x) 2 holds for the following values of x. a) x = 7/ b) x…

A: The code is written in Python and uses the NumPy and Matplotlib libraries. Here is a breakdown of…

Q: 2. Use Armstrong's axioms to prove the union rule: Ifαβ and α Y, then α-βy.

A: 2. The union rule to be proved using Armstrong's axioms are :  If α → β and α → γ, then α → βγ. The…

Q: 3 DFA->NFA In class we showed how to convert an NFA into an an equivalent DFA. Now show how to do…

A: Defined the conversion of DFA to NFA

Q: Solve the following equations using truth tables and make an observation from all its truth values.…

A: Please refer to the following steps for the complete solution to the problem above.

Q: Find minimum POS for the following Maxterm expansion. Use K-Map. F(a, b, c, d) = TTM(0, 1, 2, 3, 4,…

A: To find minimum POS using K-Map

Q: Compute a cc 5 truth table.

A: TRUTH TABLE: p q r p r T T T F F F T F F T T T F F T T T F F T T F T F F F T F F T…

Q: Prove the implication rule.That is, prove that (P → Q) ↔ (P′ ∨ Q) is a tautology.

A: Any expression with some logical notations can be stated as "Tautology" if all the expression…