Let Q(x, y) be the statement "Student x has taken class y," where the domain for x consists of all students in your class and for y consists of all computer science courses at your school. Express each of these quantifications in English. i. 3x3yQ(x, y) ii. 3xvyQ(x, y) iii. ayQ(x, y) 3YVXQ(x, y) VyaxQ(x, y) iv. v. vi. (a x)OKAXA

Definition of 3SAT : In the 3SAT problem, the input is a Boolean expression formed by m clause and n variables (each variable x can have a positive literal x and negative literal x). Each clause formed by disjunction of threeliterals and the formula is formed by the conjunction of the m clauses. For example, the following formulais an instance of the 3SAT problem: (x1 ∨ x2 ∨ x3) ∧ (x1 ∨ x2 ∨ x3) ∧ (x1 ∨ x2 ∨ x3), which is formed by 3 variables x1, x2, x3 and three clauses. The objective is to find an assignment of Boolean values to variables to satisfy the formula. In the example above, one possible satisfying assignment is to let x1 to be false and x2, x3 to be true.  Problem : A 2SAT formula is a conjunction of clauses like a 3SAT formula, except that each clause is a disjunction of 2 literals (rather than 3). For example (x1 ∨ x2) ∧ (x2 ∨ x3) ∧ (x3 ∨ x1) is a 2SAT formula.Use consistency model to provide a 2SAT formula consistent with the following labelled data (or specifythat…

Suppose X|Y=1 is a Uniform(0,4) density, X|Y=0 is a Uniform(2,6) density, and P(Y=1) = 2/3. Calculate the Bayes error, i.e., the error rate of the Bayes classifier (you may leave your answer as a fraction).

¬q → ¬ p   is called ______ of  p →q.  (contrapositive, inverse)

2. Let P(x, y) be the statement "a2 6", where the domain for a consists of all integers between -4 and 4, and the domain for y consists of all real numbers. Determine the truth value of the following propositions. (a) 3avyP(x, y) (b) Væ3yP(x, y) (c) 3y(Q(y) A VæP(x, y)) (d) 3avy(Q(y) → P(x, y)) (e) Vy(3rP(r, y) → Q(y))

Q: The propositional variables b, v, and s represent the propositions:   b: Alice rode her bike today. v: Alice overslept today. s: It is sunny today.   Select the logical expression that represents the statement: “Alice rode her bike today only if it was sunny today and she did not oversleep.”  b→(s→¬v)     2. b→(s∧¬v)   3. s∧(¬v→b) 4.  (s∧¬v)→b     Group of answer choices   A): b→(s∧¬v) B): b→(s→¬v) C): s∧(¬v→b) D): (s∧¬v)→b

x Bird(x)=Can- Fly(x) This universal quantifier used here implies that Oa. All reptiles cannot fly Ob All that flies is a Bird All Birds can fly Oc. All chicken are birds Od.

2. Determine the truth value of each of these statements if the domain of each variable consists of all real numbers. If true, give a brief explanation for why. If false, give a counterexample (i.e. a set of values x,y that make the statement false. You must also explain why they make the statement false.) a) yvx((y > x²) → y > x) b) Vy!x(√√ 0)) d) x(x < 0⇒x² ≥y) e) \xy(x² = y² ↔ y³ = x³)

12. If w is TRUE, x is TRUE, and y is FALSE, what is [((w OR X) AND (x AND y¹)) OR ((w OR x) AND (w' or y'))] AND ((x AND y') AND (w' or y'))' ? Not enough information. TRUE NULL FALSE

Construct a truth table using T and F to determine whether the argument is valid or invalid.   T: True F: False