2. Show that each of the following formulas are both satisfiable and falsifiable. (a) y Vxp(x, y). (b) Vr (p(x) V q(x)) → (Vr p(x)) v (Vrq(x)) (c) Vr (yp(x,y) →yq(x, y)).

Q: For f(a, b) = (a | b) | b (a) Simplify f(a, b). (b) Find DNF for f(a, b). (c) Is f(a, b)…

A: (a) f(a, b) = (a | b) | b can be simplified as follows: f(a, b) = (a | b) | b = b | b (since a | b =…

Q: f(x) is O(g(x)) if and only if g(x) is Ω(f(x)).

A: Proof: given: f:R---->R g:R----->R f(x) is O(g(x)) so we can say |f(x)|≤c|g(x)|.........(1)…

Q: Identify the scope of each of the quantifiers in the following wffs and indicate any free variables.…

A: The formula known as a "Well-Formed Formula" (WFF) consists of variables (capital letters),…

Q: Using the Definitional proof, show that each of these functions is O(2²). (a) f(x)= 5x (b) f(x)= 5x…

A:

Q: Show that if a, b, c, and mare integers such that m≥2, c > 0, and a≡b (mod m), then ac ≡bc (mod mc).

A: According to the question, we have to prove that ac ≡ bc (mod mc). And we have given that a, b, c,…

Q: Q.)Solve a & b and explain a. Why do we use DNF in Boolean Algebra Group of answer choices   (i)…

A: We need to find the correct option regarding K-maps and Boolean algebra.

Q: (a) [16] Let f be a function from N to (0, 1). Prove that there exists y € (0, 1) such for any n E…

A: Check below to get your answer

Q: We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now…

A: The solution is given below for the above given question:

Q: 8) Determine whether the rule describes a function with the given domain and codomain f: N→ N, where…

A: The question is to determine the given rules are functions or not.

Q: 2) Let f:R→R by f(x)=-5x²+x/2. 1) Is f one-to-one? If yes, justify your answer; if no, give a…

A: In this question we have to prove and verify f:R->R by f(x) = -5x2 + x/2 1. Is f one to one ? 2.…

Q: We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now…

A: See below step for code.

Q: No. 3 By natural deduction, show the validity of 3a (P(x) A Q(x)), Vy (P(x) → R(x)) - Ix (R(x) A…

A: Given that  3x (P(x) ^ Q(x)), Vy (P(x) → R(x)) + Ex (R(x) ^ Q(x))

Q: 4. Consider the formula A = Vx (p(x) →q(x)) → (Vxp(x) →Vaq(x)). (a) Show that A is valid. (b) Show…

A: Answer(A) :   To show that A is valid, we need to show that it is a tautology, i.e., that it…

Q: Complete the function given the variables N, a, b and return the value as "TotalArea". " "Don't…

A: Python:- Python is mostly used for machine learning Python is also used for scripting It is easy to…

Q: For f (a, b) = (a | b) | b (a) Simplify f (a, b). (b) Find DNF for f (a, b). (c) Is f (a, b)…

A: In addressing the function f(a,b)=(a∣b)∣b, we simplify it to f(a,b)=a∣b, leveraging the…

Q: Consider the Boolean function

A: Given :- In the above given question, the statement is mention in the above given question   Need to…

Q: Prove that if 3x(P(x) → Q(x) is true, then VxP(x) → 3xQ(x) is true.

A:

Q: Question 2: Let f(x):R¬R, f(x) = 2x² +5. a. Is f(x) one-to-one? Prove your answer. b. Is f(x) onto?…

A: solution to the question whether function is one one or onto or bijective is in step 2.

Q: 3. Consider the formula A = Vr (p(x) Vq(x)) → (Vxp(x) v3xq(x)). (a) Show that A is valid. (b) Show…

A: (a) To show that A is valid, we need to show that it is true for all possible interpretations of the…