Theorem 2.1 The operations A, V are commutative and associative, and the following equivalences are generaily valid: -AV B A⇒B (A⇒B) A (BA) (A^B) (AV B) AV (BAC) A^ (BVC) AV-A A^¬A 1. Avf 2. AVw 3. Anf 4. AAW A⇒B -B⇒¬A (A + B) -AV-B -AA-B (AV B)^(AVC) (A^B) V (AAC) 9 f A f A (implication) (contraposition) (equivalence) (De Morgan's law) (distributive law) (tautology) (contradiction)

Q: 3. (10) Convert the following EBNF into BNF: A := CB [x] B ::= C (xly|z) D C:= y {y D} z D:= x | y|…

A: The Answer is in given below steps

Q: 2. Recall in lambda calculus, logic connectives NOT and OR can be defined as: NOT = (Ax | xFT) OR=…

A: Answer: I have given answered in the handwritten format in brief explanation.

Q: Write the language denoted by the following regular expressions: (i) (a∗b∗)∗ (ii) a(a|b)∗a (iii)…

A: According to the information given:- We have to write the language denoted by the following regular…

Q: Prove or disprove that the language generated by the expression (OUE) 1*0+ is regular. Let 4= {a^…

A:

Q: Interpret this in plain english Φ = (a ⇒ b) ^ (c ⇒ b’) ^ (a’⊕ c)

A: Given statement is  Φ = (a ⇒ b) ^ (c ⇒ b’) ^ (a’⊕ c)  Here is the variables a,b,c

Q: i. Translate Vx[C(x) V3y(C(v) A F(xy)] into English, where C(x): x has a computer F(x y): x and y…

A:

Q: Suppose R(A, B, C) contains the tuples {(a1,b1,c1), (a2,b1,c1), (a3,b1,c1), (a2, b2, c2) (a3,b3,c3),…

A: I have provided solution in step2

Q: A, B ∈ {points} ⇒ AB ∈ Q

A: please write a full question and submit again

Q: 11. (p→ (q→r)) ↔ ((p^q)+r) 15. Determine whether the following statement forms are logi- cally…

A:

Q: Provide the definitions, some computational equivalences and also some numerical examples for ND,…

A: if  А  is  аn  n  ×  n  diаgоnаl  mаtrix: Negative Definite Matrix: Negative  Semidefinite…

Q: (1) L (abick: i, j, k≥ 0 and j = k} OS -> AK A-> aA A-> € K -> bkc S-> AK A-> aA K-> bkc K-> € OS ->…

A: The language L = {a^ib^jc^k : i, j, k ≥ 0 and j = k} consists of strings with equal numbers of b s…

Q: Write both CNF and DNF form for the Boolean expression E (x1, X2, X3, X4) = [(x1 ^ x7 ^ X4) V (X1 ^…

A:

Q: Q#4. Draw the venn diagram of 1) A-(B∪C)  2) A^c ∩ B^c

A: Q#4. Venn diagram, also called primary diagram, set diagram or logic diagram, is a  diagram that…

Q: Transform the following logical formulae into a 3-CNF. a) F: (x₁vx₂)^(-x²₂ →x₁) b) G: (X)^(-U v…

A: The CNF following the construction procedure is given by: (x1∨¬x2)∧(x1∨x2).

Q: Observe the two functions Fi and F2: F, = ĀBC + ABC + ĀBC + AĒC F2 = AB + ĀC Are these two functions…

A: Here we take some examples and put the value on it and check it.…

Q: U = {q, r, s, t, u, v, w, x, y, z}, find the computer representation for these sets;

A: Set a well-defined collection of different objects. The elements that make up a set (also known as…

Q: Newton is a brilliant mathematician and solving triangles problems fascinates him. Today he is given…

A: As per the given problem statement we have to develop a python code to determine the vertices of the…

Q: operators

A: Given :- Consider two operators A and B   Need to find the commutator of two operators for the given…

Q: Let A that A is decidable. {(G, a) | G is a CFG, a is a terminal symbol, and L(G) na' 0.} Show %3D

A:

Q: Are the functions one to one or onto only? I. f : N → Z : x ↔ x II. f : N → N : x ↔ x III. f : Z…

A: Please upvote. I am providing you the correct answer below. please please.

Q: Consider the following language: {z€ {a, b}* | #a(x) 2#(x)} (a) Give a CFG for this set. (b) Prove…

A: A grammar contain a context free grammar then it must be a context free language. Context free…

Q: Prove (two-column proof: statement reason)   (A^B) -> C (AVB) ~A -------------------------…

A: The two-column proof contains exactly two columns. One column is used to represent the statements or…

Q: Function cai (Io) should return companies whose shares are held by every investor i E I, It is…

A: Given: Base case:. cai(null) = null • Constructor case: cai ({i1, i2...in }) = {c| cE C and. ( i1,…

Q: Code must be in C/C++ language using MPI Suppose comm_sz = 8 and the vector x = (0,1,2,...,15) has…

A: in this figure show broadcast communication, In the event that we can work on the presentation of…

Q: Determine whether each of the following functions f : {a,b,c,d} -> {a,b,c,d} is one-to-one and/or…

A: One-to-one and onto are terms used in mathematics to describe the properties of a function between…

Q: Consider the following four maps: 1) 2) 3) 4) Select all, but only, the maps which are…

A: map1 map 2 map 4

Q: Answer each of the following questions. [No explanations required.] (a) What is the shortest formula…

A: Note- As per guidelines answering first three parts.  a)  Hence the shortest formula is Q.

Q: 2. Convert the following NFAs to equivalent DFAS a b →p q * r E {q,r} { } {} { } {q} {p} {r} { } { }…

A: DFA stands for Deterministic Finite Automata. In DFA, there is only one next state on an input…

Q: Let A = {-1,2, 2, 3, 12, 3} and let B = {-1,2,2 - 3, 3} a) |AUB = b) |AnB| = c) |A – B| = d) |B – A|…

A: Union - means all the element of A and B  Intersection means common element of A and B A - B means…

Q: Select the property(ies) of the given function f:Z→Zf(x)=9x+1 O fis a bijection f is one-to-one None…

A: The properties for the given function is as follows.