What equivalence/law was applied? [-p v (p A ¬q)] v [r v (q ^ ¬r)] = [(¬p v p) ^ (-p v ¬q)] v [(r v q) ^ (r v ¬r)] associativity O distributive law O commutativity O domination law

Q: All negative integers are less then zero. -56 is a negitive integer . Therefore, -56 is less then…

A: All negative integers are always less than zero.

Q: i) Determine the domain of ) (x). In 1-2 sentences axnlnin

A: Solution is attached below.

Q: 4) Consider the equivalence claim: (Vx € R)(3! y E R)P(x,y) = (3! y € R)(Vx € R)P(x,y). (4.1) What…

A: Given equivalence claim is ∀x∈ℝ∃! y∈ℝPx,y≡∃! y∈ℝ∀x∈ℝPx,y The domain of a predicate is the set of all…

Q: The biconditional statement "x2 = 4 if and only if %3D x = 2" is false. Split the statement into…

A: Given statement x2=4 ⇔x=2

Q: What property is symbolized in the image below? * If * then Reflexive Associative Symmetric…

A:

Q: of the propositional equivalences. Don't use a truth ta

A: Introduction: The following equivalence laws, we will use in this problem. The implication law…

Q: Let x, y ∈ Z. (a) State the contrapositive of the statement: ♠ If xy and x + y are even, then both…

A: Contrapositive for the statement "if A then B " is "if not B then not A" Given statement:   If xy…

Q: pVq Select the argument that is invalid.

A: Introduction: A truth table is a logical table that is used to determine whether a compound…

Q: There will be three columns. The first column is for Premises of formula, the second column contains…

A: Consider the provided question, We have to prove that the given statement. (3) To Proof,…

Q: Evaluate: Premises: 1. "DISCRMT is difficult or not many students like DISCRMT." 2. "If CALENG is…

A: Given that, Premises: 1. "DISCRMT is difficult or not many students like DISCRMT" 2. "If CALENG is…

Q: Prove using truth table KB a ?

A: Here given three variables a, b and c  So using 3 variables truth table derive result

Q: Suppose a Knowledge Base (KB) agent having premises is as follows: 1. If it is humid, then it is hot…

A: given , premise 1 if it is humid, then it is hot . premise 2 if it hot and humid , then it will…

Q: Find projvu.u = (0, −1, 2), v = (3, 2, 4)

A:

Q: are even. If x is even, then x y is even. (use indirect proof

A: X and y be two integersLet x is evenTo Prove x y is evenAs x i even Then x = 2k ,  K ∈ z∠and y ∈z…

Q: 19) Define an appropriate language and formalize "There is a student who is loved by every other…

A: Given Statement "There is a student who is loved by every other student" Third FOL formula is…

Q: 3. Prove or disprove: U(8) Z.

A:

Q: 5) Verify the logical equivalence (p ^q^ ¬r) V (¬p ^ q ^ ¬r) = q ^ ¬r by using known logical…

A: ACCORDING TO BARTLEBY GUIDELINES, SOLUTION OF ONLY FIRST QUESTION WILL BE PROVIDED.

Q: Prove using the sequent calculus that (pAq) V-p V ¬g is a tautology.

A:

Q: The inductive step of an inductive proof shows that for k > 4 , if k! > 2k then (k +1)! > 2k+1…

A:

Q: 3. RewriteANBCB with quantifiers and prepositions.

A: An element a is contained in the set A then it can be denoted as a∈A. Mainly there are two types of…

Q: Use either the soundness or the completeness (Post's theorem) of the propositional logic to prove ¬A…

A: Soundness Theorem: If P|-Q then P|=tautQ. In words, soundness theorem says that if P implies Q then…

Q: Determine if the statement is an "inclusive or" or and "exclusive or" A password must have at least…

A:

Q: How to express the commutativity of V as a tautology?

A:

Q: Which is the contrapositive of A==> B? (a) B ==> A (b) -,B ==> A (c) -,B ==> -,A (d) -,A…

A: Which is the contrapositive of A==> B?

Q: Construct a formal proof of validity by adding only three statements to the given premises using the…

A: We prove the given argument by using rules of inference.

Q: hen statements then apply statements using converse inverse and contrapositive on the issues.…

A: Introduction: A conditional statement has two parts: an "if" clause with a hypothesis and a "then"…

Q: Note that “a sufficient condition for s is r” means r is a sufficient condition for s and that “a…

A: The given statement is : “A necessary condition for this computer program to be correct is that it…

Q: why don't we use the existential instantiation(∃x) instead of the universal because it says "A car"…

A: A convertible car is anonymous, whose it is; which company; how many in the locality, city, country;…

Q: Write the negation of the statement “0 < 1” in five different ways. Four of those ways should steer…

A:

Q: Find projvu.u = (2, 3), v = (0, 4)

A: Given: Let the vector u and vector v be: Formula used:

Q: prove PV (QAR) = (PVQ) A (PVR) without using Truth table.

A:

Q: Find projvu.u = (2, 5), v = (0, 5)

A:

Q: Explain the logic of a Kruskal–Wallis test.

A: Kruskal-Wallis test: The Kruskal-Wallis test is useful for comparing the means of the population…

Q: An inventory consists of a list of 115 items, each marked “available” or “unavailable.”  There are…

A: Consider the given information.

Q: 4) Prove that (X.Y +X.Y) = (X Đ Y) using truth table? %3D

A:

Q: This rule of logic is true when both of its conjuncts are true, and false otherwise. Which law of…

A: Solution

Q: Use the contrapositive to rewrite the statements in if-then form in two ways. Being divisible by 3…

A: Recall that “If P then Q” means “P is sufficient for Q” and “Q is necessary for P” to happen.…

Q: Suppose that A ==&gt; B is true. Which is then automatically true, the converse or the…

A: Suppose that A implies B is true. The converse of implications, A → B will be written B → A . The…

Q: Evaluate: Premises: 1. “DISCRMT is difficult or not many students like DISCRMT." 2. "If CALENG is…

A: given premises 1.) "DISCRMT is difficult or not many students like DISCRMT". 2.) "if CALENG is easy…

Q: In a study of pain relievers, 100 people were given product A, and 71 experienced relief. In the…

A: Given that, 100 people given product A and 71 experienced relief. Also in same study 25 people given…

Q: A negation for “Some R have property S” is “

A: The given statement is Some R have property S.

Q: Evaluate: Premises: 1. "DISCRMT is difficult or not many students like DISCRMT." 2. "If CALENG is…

A: Given Premises is as follows, 1. "DISCRMT is difficult or not many students like DISCRMT" 2. "If…

Q: can you please write this in a two column proof involving statements and reasons. Thanks you.

A: To prove: ABCD is a parallelogram If we can show that the opposite angles of the given…

Q: Find the term involving in the exp ansion of (4x- -;). 130 140 x2 x2 Option 1 Option 2 150 160 x2 x2…

A: The general term that is the (r+1)th term in the expansion of a+bn is nran-r br.  The formula for nr…

Q: 2 Prove that logical eauivalent or not filleusing in expression 2.

A: Given,           expressions are-                       and

Q: 3. How to express the associativity of V as a tautology?

A: Tautology is a preposition that is always true.

Q: Let X = {a, b, c} and R={(c, b),(a, c)}. Then Check the all properties reflexive,symmetric,…

A: