a) Express the following statement using predicates and quantifiers. "Everybody must take a discrete structure course or be a computer science student."

Q: Let P(x), Q(x), and R(x) be the statements “x is a professor," “x is ignorant," and "x is vain,"…

A: We are entitled to solve only first three subparts of a questions so, I am providing you the same.…

Q: Consider the following assertions about the sets A, B and C. Write them down in the language of…

A: Given: The construction of predicate logic is as follows, ∀, ∃, ¬, ⇒, ∧, ∨

Q: ii) V(x, y € Z)(x? + y? > 0).

A: We need to check for all x and y which are integers, the predicate x2+y2>0 is true or not.

Q: Construct a Boolean expression having the given table as its truth table. PQRS 1 1 1 0 1 0 1 1 10 10…

A:

Q: make a predicate logic proof 1. (x)(Ax Ɔ Bx) 2. (x)[(Ax • Bx) Ɔ Cx]/ (x)(Ax Ɔ Cx)

A: (1) (x)  (Ax→(Bx and Cx)                     / (x)(Ax→(x)(2)  Aa→(Ba and Ca)…

Q: 9. Let P denote the open sentence "x € A" and let Q denote the open sentence "x € B". (a) Write "x…

A: Introduction: If two logical statements have the same truth value in all circumstances, they are…

Q: 1. Determine which of the following statements are true for all sets A, B, C, and D. If a double…

A: .

Q: Express the following concepts in description logic using atomic concepts Hospital, Patient,…

A: Due to company policy, we can solve only the first three sub-parts, as this is a multipart question…

Q: Exercise 5 1. Using truth table prove that: a) {(X © Y), Y} | = ¬X (where "O" designates the…

A: a) The statement is X⊙Y,Y|=¬X. The truth table is X Y X⊙Y X⊙Y,Y ¬X T T T F F T F T F F F T…

Q: Convert the following scenario into first-order predicate calculus. Anyone passing his Discrete…

A: As per the instruction, we will convert the following scenario into first-order predicate calculus.…

Q: Translate each of these statements into logical expressions using predicates, quantifiers, and…

A: # As per the guidelines we are entitled to solve three subparts , please submit the other parts if…

Q: 2. Translate each of these statements into logical expressions using predicates, quantifiers, and…

A: We will answer the first three subparts of the given question as per our guideline. Please resubmit…

Q: Construct a truth-table for the following compound propositional logic statement

A: Consider the given expression. ~P∨Q↔~P∧~Q

Q: Define the following logical connectives and give one each example: 4. Conditional 5. Bi-conditional…

A: Logical symbols

Q: Given the following definitions: • S: the domain of all CPSC 121 students. • G: the domain of all…

A: The first statement is  ∀x∈S, ∀g∈G, Ax,g↔Bx In this statement the scope of ∀x is the entire…

Q: b) Let I be a set of formulas and let y be a formula of Predicate Logic such that CEVry and TEy.…

A: we have  Γ |-∀xφ and Γ |-∀x¬φ Now, Γ |-∀xφ ∧∀x¬φ⇒Γ |-∀xφ ∧¬φ⇒Γ |-∀xFalse

Q: 4. Use the properties of Logical Equivalences and your class slides to draw the circuit of the…

A: Given the expression is P ↔~Q.

Q: Let P(r) and Q(r) be predicates with one free variable, namely r. With explanation, are Vr (P(x)…

A: Given that Px and Qx are predicates in the free variable x. Note that, a predicate and its negation…

Q: Let U (universe of discourse) be the set of all people. P(x,y): x and y are each other's classmates…

A: Let U (universe of discourse) be the set of all people. Denote: P(x, y): x and y are each other's…

Q: Determine whether the following statements are logically equivalent. Provide a justification for the…

A: We have to show whether ~p∨~p∧q   and  ~p∧~q are equivalent or not.

Q: Let W(x) be the statement " x weighs more than 4000 kg", where the domain is the set of all…

A:

Q: 4. Draw the logic diagram corresponding to the following Boolean Expression. a) (P+ R)• (Q ® R))+ (P…

A:

Q: In this section, U will denote the universal set: the set of students at some university. S will…

A:

Q: Negate the given statement by changing the existential quantifier to a universal quantifier, or…

A: given statement every house is a home , no house is a home , all books are blue claim to negate the…

Q: A is a tautology if and only if NotA is unsatisfiable. Prove

A: Some definitions: Definition 1: A (truth) valuation is a function v that assigns truth values. For…

Q: Let W(x) be the statement " x weighs more than 4000 kg" , where the domain is the set of all…

A: Given: Domain is set of all elephants. Wx: x weighs more than 4000 kg. To do: Translate the…

Q: Let C(x) denote the predicate "x is in the correct place". The translation of the statement :…

A: Given problem Given that   Let C(x) denote the predicate " x is in the correct place ". The…

Q: Write the following statement in predicates using quantifiers: (i) The product of one odd and one…

A: Given statement "The product of one odd and one even integer is odd" we want to write in predicate…

Q: (P → Q) ^~ (~PVQ)

A: We need to construct a truth table for P→Q∧~~P∨Q Now, if we have a statement P, then the negative of…

Q: Show that (B- A)U (C-A) = (BU C)- A 1) Using Venn diagrams 2) Using the set-builder notation and…

A:

Q: 2.2. Write the following statements in symbolic form using universal and existential quantifiers,…

A: Universal quantifier is denoted by '∀' and is called as 'for all' and existential quantifiers is…

Q: Use set builder notation and logical equivalence to establish the De Morgan law (AUB) ̅=(A ) ̅∩B ̅

A: A∪B¯=x| x∉A∪B             =x| ¬x∈A∪B             =x| ¬x∈A∨x∈B             =x| ¬x∈A∧¬x∈B…

Q: A discrete mathematics class contains 1 mathematics major who is a freshman (1st year), 12…

A: Let, Mx: x is a mathematics major. Cx: x is a computer science major. Jx: x is a junior. Sopx: x is…

Q: Create a truth table to show all possible inputs and outputs for the Boolean function described by…

A:

Q: Let T(s) denote s is a technologies major, C(s) denote s is a computer science student and E(s)…

A: handwriting solution

Q: Prove the following statement using an element-chasing argument. If ACBUC and AN B= Ø then A C C.

A: Let x be any arbitrary element in the set A.  Then as A is a subset of B U C, x must be an element…

Q: a. Write the negation of the following statement without using ¬. (3x E Z)(Vy E Z)(3k € Z)(x + y =…

A:

Q: Translate the statements using quantifiers: 1-No English majors like taking Chemistry classes…

A: Symbols given are as follows: Sx: StudentAx: Majoring in AviationRx,y: y is roommate of xLx:…

Q: Show that (p a q) → (¬ p → q) is a tautology. Show that (p → q) ^ p and (q ^ p) are logically…

A: Truth table is used to show the two statements are equivalent

Q: Is 8-8=0 a universal or existential quantifier.

A: Let us first go through the definition of  universal and existential quantifier as well as universal…

Q: . Express the following English sentence with predicate logic using Existential and/or Universal…

A:

Q: If the domain consists of all animals, express the following statements in terms of quantifiers and…

A: Given that domain consists of all animals.

Q: 8. Use quantifiers and predicates with more than one variable to express this statement: "There Sa…

A:

Q: Let the universe of discourse, U, be the set of all people, and let M(x,y) be “x is the mother of…

A: It is given that M(x,y) be “x is the mother of y.” (1) (∃x)U((∀y)U(M(x,y))) It states that "There…

Q: 4. Express each of these statements using predicates, quantifiers, logical connectives, and…

A: We know that ,  A Predicates is an expression of one or more variables defined on a some specific…

Q: Use truth table to verify the following logical equivalence. (p →g) ^ (p →r) =p→ (qar)

A:

Q: Which of the following best describes what is a Major Clause? O a. None of the other alternatives. O…

A: Explanation: A clause in a predicate is called major clause if it determines it's predicate iff…

Q: 4. Let the universe of discourse, U, be the set of all people, and let M(x, y) be “x is the mother…

A: Answer :

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.