The proposition p <-> q is logically equivalent to a. [(NOT q> NOT p) AND (q -> p)]. -> O b. [(p > NOT q) OR (q -> NOT p)]. c. [(p-> NOT q) OR (NOT q -> p)]. O d. [(NOT p -> q) AND (q -> NOT p)].

Let the domain be the set of all animals. Define the following predicates: A(x) : x can add. • W(x) : x can waltz. • D(x) : x is a dog. • C(x) : x is a cat. Translate each of the following logical expressions into English. 1. Vx(D(x) → (A(x) V W(x)). 2. Ex(C(x) A ¬A(x) ^ W(x)) 3. -3x(D(x) ^ A(x)) 4. Vx((D(x) V C(x)). → W(x))

Racket code only please Using the logical operators, and, or, implies, not, and iff, and atoms representing truth values, we can make a list that would represent proposition: For instance: '(A and (not A)), or '((B iff (A or C)) implies (not (C implies A))) would represent the formal statements (?∧¬?) and ((? ≡(?∨?)→¬(? →?))). We use the following convention when we represent propositions in this way: for every operator – unary or binary – there corresponds at least one pair of parentheses defining its scope (and perhaps more). Thus, the lists ‘(A and not A) and (B iff A or C) are not permitted but ‘((A and ((not A))) and ‘(B iff (((A or C)))) are acceptable. Define Evaluate-WFF, which will take as input a formula of prepositional logic in which there are only truth values and no propositional variables, such as the following: (#t or (not #t)). Evaluate-WFF should return #t if the formula under the particular truth assignment evaluates to #t and false otherwise. By way of example,…

Racket code only please Using the logical operators, and, or, implies, not, and iff, and atoms representing truth values, we can make a list that would represent proposition: For instance: '(A and (not A)), or '((B iff (A or C)) implies (not (C implies A))) would represent the formal statements (A∧¬A) and ((B ≡(A∨C)→¬(C → A))). We use the following convention when we represent propositions in this way: for every operator – unary or binary – there corresponds at least one pair of parentheses defining its scope (and perhaps more). Thus, the lists ‘(A and not A) and (B iff A or C) are not permitted but ‘((A and ((not A))) and ‘(B iff (((A or C)))) are acceptable. 1. Define collect-prop-variables, which will take as input a list representing a proposition, and return a list, representing a set, of all the variables used in the expression. Example: (collect-prop-variables '(A and (not A))) should return '(A) and (collect-prop-variables '((B iff (A or C)) implies (not (C implies A))) )…