Express the following sets using the roster method. Express the elements as strings, not n-tuples. (a) (b) (d) {0x: x € (0, 1)²} (c) (Ox: x € B), where B = {0, 1)0 u (0, 1)¹ u {0, 1)². (o) {0, 1}0 U{0, 1}? U{0, 1}2 {xy: where x € (0) U (0)² and y € (1) u {1}²}

Q: Find the dual of the Boolean expression T+r.0+ ryz O T.(T+0). (T +y+ z) O r. (r.1). (T + y+ z) O…

A: The dual of Boolean expression is given as follows :

Q: 3. Simplify the following Boolean expression: а. (х + у) z' + y(x'+2') b. x'z (xy + y'z' + yz) с. у…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Let the domain of x and y be all people, Let W(x): "X is a woman". M(y): "y is a man", and L(x.y):…

A: Given W(x): ' x is a woman' M(y):' y is a man'

Q: simplify the following boolean expressions with postulates and theorems. clearly state each step and…

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Q: Determine whether the following are linear trans- formations from R³ into R²: (а) L(x) 3 (х2, хз)"…

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Q: The equivalence of the Boolean expression: z= x(x+ y) is A z= x(xy) B z=xy C := xy D :=x(xy)

A: Given Boolean expression                                                        z=xx¯+y¯ we have to…

Q: Let M(x) = V3x – 6 and N(x) 2 Find the following: 2 - c) (N o M)(5) d) (No M)(홍) e) (No M)()

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Q: Translate ap(F(p) ^ B(p)) → ajLj) into English where F(p) is "Printer p is out of service," B(p) is…

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Q: 2 > ]x – 4| X-1

A: Given,          2x-1≥x-4

Q: Let a (1) b=(1 1 1), A= Determine each of the following: A (a) a (b) A b (c) 12 ⓇA (d) A 12 (e) AⓇA…

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Q: Which of these statements is the inverse to Vx e People, HavePhD(x) A Teachln(x, university) →…

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Q: Let x={1,2,3,4} and y={1,2,3,4,5,6,7,8,9,10}   and "f" from X to Y is given by…

A:

Q: Define two operations + and * on A = Z × Z as follows: for (a, b) and (c, d) in A: ɔy (a, b)+(c, d)…

A: As per guidelines, we will solve first three subparts: Define two operations + and * on A=ℤ×ℤ as…

Q: Let F(x,y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The…

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Q: 5. Let A = {a,b} and B = {1,2,3}. (a) Write out all functions f: A → B using two-line notation. How…

A: Note:-  As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Let a=⟨−3,−2,2⟩ and b=⟨−4,−2,0⟩ Compute:

A: Given that          a = <-3, -2, 2 >    and    b = <-4, -2, 0> Here we have to compute…

Q: Complete the table to express the values of each of these Boolean functions. F(x, y, z) xỹ + (xyz)…

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Q: A. Use laws of Boolean algebra to simplify the following Boolean expression [(XY') +Y']'

A: Using De Morgan formula and other laws of Boolean algebra: XY'+Y''=XY''Y''…

Q: Consider the truth table for the connective '' with two simple declarative statements p and q. Р q T…

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Q: Let F(x,y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The…

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Q: In the following wff, there are six occurrences of x. From left to right, which most accurately…

A: An occurrence of x is bound if it occurs in either ∃x or ∀x or in their scope. Otherwise the…

Q: Let the domain of x and y be all people. Let W(x): "x is a woman", M(y): "y is a man", and Lex.y):…

A: The objective is explain the meaning of the statement ∀x∀y Wx∧My→Lx,y

Q: Let Q(x, y) be the statement "x + y = x - y." If the domain for both variables consists of all…

A:

Q: select the description that characterizes the Boolean expression

A: A boolean expression is CNF (Conjunctive normal form) if it is a product of sums. And, a boolean…

Q: Determine the orders of the elements of D∞

A: It is known that, D∞=a,b|a2=b2=e also it can be observed that, D∞=abka,abk,bak,bakb Let x∈D∞. If…

Q: Let S be the set of all strings of a's and b's of length 3. Let B = {0, 1}. Let f: S B be defined as…

A: S be the set of all strings of a's and b's of length 3 . Then to find f(aaa) , f(aab) , list all the…

Q: Let R(a, b, c), S(a, b, c), and T(a, b, c) be three relations. Write one or more Datalog rules that…

A: Given (R∪S)-T The solution for (R∪S) is as follows ∪(a,b,c)←R(a,b,c) OR S(a,b,c)--------(i) The…

Q: Express the following statements using quantifiers; logical connectives, assume proper predicate…

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Q: F = ABC + ABC' + A'B (i) F=(A+B)' (A'+B').

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Q: 3. Let V be the set of all ordered triple in R³, and F, the set of real numbers, where the…

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Q: (c) Using the set identities, prove that (A – B) n (A – C) = A – (B U C).

A: To Prove: A-B∩A-C=A-B∪C

Q: d. AAB (The symbol denotes the symmetric difference operator for sets, defined as follows: AAB = (А…

A: Since you have asked for a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Select the description that characterizes the Boolean expression: xỹz CNF and DNF CNF, but not DNF…

A: Conjunctive Normal Form (CNF) is an expression which is intersections of unions. Disjunctive Normal…

Q: The first-order logic formula vx A(x)^3y -A(y) is satisfiable but not valid

A: Given that a first order logic formula ∀x A(x)∧ ∃ y¬A(y). We need to check that is it valid,…

Q: Q 4. (a) Prove or disprove that for any real numbers x and y, [x + y] = [x] + Lyl (b) Find the…

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