Consider unit propagation starting from the following clauses: {¬a,b}, {a,¬b,c}, {a,b,¬d}, {¬a,¬b}, {¬c}, {c,e}, and {c,¬d,¬e}. Which of the following literals can be inferred by unit propagation? 1. a=True 2. b=False 3. d=False 4. e=True

Q: Provide a counterexample for the statement: For any sets A,B and C, А - (В -С) — (А - В) — С.

A:

Q: Check whether these statement are consistent or not: a. ¬(p Vq) and (pq) b. rqAr and ¬(qV¬r)

A: Introduction: Two propositions are referred to as consistent when their truth values are same at…

Q: Given r = {(0,0), (0, –1), (1, 1)}, select all true statements. Orl = {(0,0), (–1, 0), (1, 1)} OD,-1…

A: topic - functions and inverse functions

Q: Show that (p-q)–(r¬s)and(p-r)-(4-s) are not logically equivalent.

A: To show that p→q→r→s and p→r→q→s are not logically equivalent.

Q: e. Show that ¬(p → q) and ¬p → q are logically equivalent. f. Show that (p → q) ^ (p → r) and p → (q…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: Construct the truth tables for the following compound prepositions. a. [(a V b) V c] → [a V (b V c)]

A:

Q: Let p, q and r be statements. Here "-" means "negation"; "" means "is equivalent"; "=" means…

A: Tautology : A sentence whose truth table contains only 'T' is called a tautology. Options a,h and i…

Q: Write the contrapositive converse and inverse of the following statement, in words and in symbolic…

A: Let a statement be defined as: "If p, then q."  The converse of this statement is "If q, then p."…

Q: 4. Let S = {students at your school}, M = {released movies}, and let A(s, m) be the statement…

A:

Q: All the employees at the Acmesoft company are either programmer or salespeople.The programmers…

A: There are two employees. They can be both programmers, both sales person, one programmer and one…

Q: Consider the proposition P(a, b, c) in the variables a, b, c E R\{0}: alb a P(a, b, c) : blc C Which…

A: We have to choose which statement is true for the given case:

Q: Which of the following is CONTRADICTION? A (¬Pv P)A¬P B (¬(¬Pv P)) ^P (¬Pv P) v ¬P (D (¬(¬PAP) AP

A:

Q: For a  conditional statement, the contrapositive of the converse is always logically equivalent to…

A: Introduction: Consider the conditional statement: "If A occurs, then B occurs".

Q: ' Suppose that you are given the following logical statement - A V B + ¬ C ^ D on our discussion of…

A: Given logical statement, ¬A∨B↔¬C∧D Firstly, The order of operation is to be determined.

Q: Suppose that P(x, y) is a predicate with two free variable, x and y. Let the domain for x consist of…

A:

Q: 2. Construct the truth tables for the following compound prepositions. b. [(u → v) ^ (u → w)] → (u →…

A: We will use following truth values to construct truth table u v u∧v u→v T T T T T F F F F T…

Q: Use the laws of logic to show that ((s V¬r V¬q) ^ (¬s V r V s) ^ (¬r V¬s V¬q)) = ¬(q ^r).

A: Given statement is  s∨¬r∨¬q∧¬s∨r∨s∧¬r∨¬s∨¬q  -----------(1)     consider  ¬s∨r∨s ≡ ¬s ∨s∨r    (…

Q: Let A = {2,4, 6, 8}, B = {3,4,5,6} and D = {4,5}, Which of the following statements is/are true?…

A:

Q: Determine whether each of the following  statements are True or False and why:…

A: 1) False. A set A is a subset of a set B if and only if every element in A is in B.For any sets A…

Q: Given statement: "If x is positive or x is 0, then x is nonnegative." Write its negation,…

A: The given statement: "If x is positive or x is 0, then x is nonnegative." We have to write the…

Q: In this activity, you want to find a statement S so that ((AVB)^¬A) = S is a tautology. (a) Complete…

A: Since you have posted a question with multiple subparts, we will solve the first two subparts foryou…

Q: If AOCD N AJAL, then which of the following statements are true? Select True or False for each…

A: Two triangles are congruent if their corresponding sides are equal in length, and their…

Q: 8. The following argument form is invalid. Construct a truth table to show why this is, indicating…

A:

Q: Question 6. Let S, T and U be three sets. (1) Write the statement SnT U using the logic symbols (but…

A: Given: S, T, and U are three sets. To Do: (a) Write the statement S∩T⊈U using logic symbols. (b)…

Q: What is the dual of (A A B) v (C A D)? * O (A V B) (C v D) O (A V B) v (C A D) O (A A B) v (C v D) O…

A: We want to find dual of (A∧B)∨(C∧D)

Q: For each statement below, determine whether it is a tautology, contradiction, or neither. Justify…

A: A compound proposition that is always true for all possible truth values of its variable or in other…

Q: 3. Given the following predicates: • C(x): x is a CS student • L(x): x loves programming where the…

A: It is given that

Q: Consider the statements (P → q) and -P→ ¬q_ a. Are they logically equivalent? b. Justify your answer…

A:

Q: The table below shows the values of predicates

A: Given,

Q: b) Let A = B ={-2,-1,0,1,2}. Write negations for the following statements and determine which is…

A: Answer : In Both case only negation are true

Q: 3. Prove that: 7: (not (for all x)(p(x, f(a))) if and only if ((for some x) not p(x, f(a))) is a…

A:

Q: What is the conditions to make clause “b” as major clause.

A: Given: p = a ˄ (b ˅ c )

Q: a 2. Consider the open sentence P(a, b) : > 1., where the domain of a is A = {-4,3,5} and the domain…

A: This question is about discrete mathematics.

Q: Let A = (2,-1,4), B = (3,0,6), and C= (-1,-2,-3). Is it possible to construct AABC? Show your logic.

A: The given points are A=(2,-1,4), B=(3,0,6), and C=(-1,-2,-3). We need to justify whether it is…

Q: Q7. Let x and y be propositional variables, and let P₁: zvy P₂: x^-y Ps: yr C:y Answer the following…

A:

Q: a 1. Consider the open sentence P(a, b) : > 1., where the domain of a is A = {-4, 3,5} and the b…

A: