Solve the following equations using truth tables and make an observation from all its truth values. [p^(pvq)] → P • [p^ (q→ 1)] → (q→r) ● [(pvq) ^ (pr) ^ (q→ 1)] → r (pq) v (qr) V (rp)

Q: 37. Construct a truth table for each of these compound sitions. a) p→ (-q Vr) b) ¬p → (q→ r) c) (p…

A: First lets understand how each operator works: ∧ : And operator: p∧q : is true when both p and q are…

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: 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: 1. Write the ô function of the following (1) dfa S NFA : Q×(EU{1})→P(Q) ) respectively, where…

A: Given : DFA and NFA The task is to convert these components into the state table function.

Q: Show 3x[p(x) A q(x)] E 3xp(x) ^3xq(x)

A: To prove: Prove that ∀x(P(x) ∧ Q(x)) is logically equivalent to ∀xP(x) ∧ ∀xQ(x)

Q: Suppose g: RR where g(x) = [™=¹] a) If S = {x|1 ≤ x ≤ 6}, find g(S) b) If T = {2}, find g¯¹(T) .…

A: Suppose  where List the answer for eacha) If, find  b) If , find

Q: Implement the function by simplifying and creating a truth table. F(W,X,Y,Z)= ((W^X)) | (~(Y&Z))…

A: The given function is: F(W,X,Y,Z)= ((W^X)) | (~(Y&Z)) where ^ (XOR), | (OR), ~ (inverse) and…

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: 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: Find the truth sets for M(x) ^ N(x) using N and Z

A: Using the N universal set: The N universal set consists of all positive integers from 1 to infinity.…

Q: Find minimum POS for the following Maxterm expansion. Use K-Map. F(a, b, c, d) = TTM(0, 1, 2, 3, 4,…

A: To find minimum POS using K-Map

Q: Find a countermodel for each of the following wffs: 3x p(x) → Vx p(x) Væ (p(x, f(x)) → p(x, y))

A: Counters are an uncommon instance of limited state machines since they move straightly through their…

Q: Compute a cc 5 truth table.

A: TRUTH TABLE: p q r p r T T T F F F T F F T T T F F T T T F F T T F T F F F T F F T…

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

A:

Q: f(A,B,C,D) = Em(2,3,4,5,7,8,10,13,15)

A: f(A,B,C,D) = Em(2,3,4,5,7,8,10,13,15)