For the following pairs of expressions, find a unifier for each pair if a unifier exists. If a unifier does not exist, explain why. (a) p(X,Y) and p(a,Z) (b) p(X,X) and p(a,b) (c) f(X,Y) and f(a,g(a)) (d) q(X) and ¬q(a)

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: ! Exercise 3.2.4: Show that each of the following are not valid rules about FD's by giving example…

A: The answer for the above mentioned question is given in the following steps for your reference.

Q: We can think of a logical operator and its associated truth table as a function. For example, we can…

A: The question is how many different logical operators could we define for two propositional…

Q: Improve the following deadwood expressions. Example: at the present time – now   Acknowledge…

A: The deadwood expressions are  improved in the below step

Q: Write the following English statements using the following predicates and any needed quantifier. The…

A: We are given two English statements and few predicates. We are asked about the logical statements…

Q: VX(P(X) v Q(X)) –→ (VXP(X) V VXQ(X)) The above expression follows from the valid argument forms of…

A: Solution:   Given,

Q: (a)~ (PAP) (b) QV (P⇒Q) (c) ((PVQ) AR) ⇒ (PV¬R)

A: Given compound statements are  (a) ~(P /\~P) (b) QV (PQ) (c) ((PVQ) /\R) = (PV¬R)

Q: Which functions are one-to-one? Which functions are onto? Describe the inverse function for any…

A: This is a question about one-to-one, onto, and bijective functions and their inverses. The question…

Q: 3. Determine whether the Boolean operator, that is defined by: is: x 1y = (xy)' a. COMMUTATIVE: Give…

A: Given: X ↑ Y  =(XY)'

Q: Let Γ be a set of sentences of L1 (the language of propositional logic) and let φ be a sentence of…

A: Let Γ be a set of sentences of L1 and φ a sentence of L1. The argument with all sentences in Γ as…

Q: Complete the truth table for the implication. You must submit a complete TT. (A ∧ ~B) → C. A B…

A: According to the information given:- We have to complete the mentioned truth table of (A ∧ ~B) → C.

Q: Tick each statement that is valid. Select one or more: a. ¬(C → (D → C)) is unsatisfiable. b. Av¬Bv…

A: Solution   The given each statement is coming under propositional logic. It is concerned with the…

Q: Simplify the following Boolean functions with K-maps to the indicated number of literals (in…

A: Hi please find the solution below and I hope it would be helpful for you.

Q: Write the following English statements using the following predicates and any needed quantifier. The…

A: 1. Some students have not asked any faculty member a question ∃x(S(x)∧∀y(F(y)→~A(x,y)))…

Q: Proposition (Distributive Law): For expressions P1, P2, P3, any word matching the regular expression…

A: Proposition(Distributive Law) According to the Distributive Law, multiplying an amount by a set of…

Q: What’s the language of the regular expression b, i.e., the set of all strings that can be recognized…

A: What is a Regular Expression?A regular expression (regex) is a sequence of characters that defines a…

Q: Proposition (Distributive Law): For expressions P1, P2, P3, any word matching the regular expression…

A: The above equation is true and the explanation is given below.

Q: me predicates and their corresponding statements: p(x): x is a student in your class q(x):…

A: Given     p(x): x is a student in your class                q(x): x has taken a course in logic…

Q: p q r ∼q∼q p∨∼qp∨∼q ∼p∼p r∧∼pr∧∼p (p∨∼q)→(r∧∼p)(p∨∼q)→(r∧∼p) T T T                     T T F…

A: Solution- According to the given statement we completly created the truth table and predict that…

Q: Determine the truth value of each of the following statements if the domain consists of all…

A: Step 1: Step 2: Step 3: Step 4:

Q: Given the language L = {bamb"a, (ab)", aa: n,m > 0 and h 21}, find the regular expression r such…

A: Regular expression is a linear sequence of symbols and characters that represent the given string or…

Q: (∀x, y, z, w)(B(x, y, z) ∧B(w, y, z) →B(x, w, y)).

A:

Q: a. Correctness of dynamic programming algorithm: Usually, a dynamic programming algorithm can be…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Construct proof for the following argument within the system of sentential logic: 1. (A & B) ⊃ (C V…

A: To prove the argument using the rules of sentential logic, we'll apply logical deductions step by…

Q: Form the negation of the following statements. Then apply De Morgan's law and/or conditional law,…

A: The answer to the given question is in subsequent steps.

Q: Let K(x, y) be the statement "x knows y", where the universe of discourse for both x and y is the…

A: For translating this sentence, we will use Existential quantifier ∃, read as "there exists"…