Let g: A → B and f:B → C Prove that g is one-to-one if f og is one-to-one

Q: Let B={x∈R|x5∈Q} be a set. Is B countable? Justify the answer by showing the explicit formula for…

A:

Q: Suppose that the domain of the propositional function P (x) consists of the integers 1, 2, 3, 4, and…

A:

Q: Suppose that the domain of the propositional function P(x) consists of the integers -2, -1, 0, 1,…

A:

Q: Prove that for every real number b, where b is not equal to 0,= b.

A: Given

Q: (c) In the proof of Proposition 3, the following statement is not justified: "However, since x is…

A:

Q: 1. Translate each of the following sentences into symbolic logic, then find their negation. (a)…

A: (a) x is a person p(x) = x is majoring in math q(x) = friend who needs help with their homework The…

Q: B. Use the method of direct proof to prove the  statement 2. If x is odd, then x2 is odd.

A: Given: If x is odd, then x2 is odd.

Q: Which of the following mathematical statement corresponds to the statement: "If there exist a real…

A:

Q: 6. Let A = {x EZ|x= 5a+2 for some integer a}, B = {y €Z|y= 10b – 3 for some integer b}, and C = {z…

A: Here  A =x∈Z| x=5a+2 for some integer a ,B=y∈z|y=10b-3 for some integer b    C=z∈Z | z=10c+7 for…

Q: create a proof for the following argument. 1.G ⊃ ∼∼H 2.G • ∼(K • H) ∼K

A: Using the rules of inference we prove the given argument.

Q: Prove that for every real numbers a, b, and c, where b a is not equal to zero, if a +b = c, then=+1

A: Given,            For every real numbers a,b and c, where b is not equal to zero.            if…

Q: Construct a formal proof in proving the following argument. Follow the steps presented in this…

A: The variables given for our problem are as follows: w→Workm→MoneyI→Idlee→Enjoy The terminologies we…

Q: 4. Determine the truth value of each of these statements if the domain consists of all real numbers.…

A:

Q: Prove by contrapositive. if x and y are integers such that x > 1, and x divides y, then x / (y +1)

A:

Q: Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p…

A: topic - functions

Q: Prove that there exists irrational numbers r and y such that x" is

A:

Q: 2. For all real numbers a, b and c, prove that if a <b <c then a+b+c a < 3 < C.

A: given that a, b, c are real numbers we have to prove that if      a&lt;b&lt;c    then…

Q: Suppose f(x)=2.1⋅x6f(x)=2.1⋅x6 and g(x)=−0.5⋅x3g(x)=-0.5⋅x3. Which of the following statements is…

A: Given that: f(x)=2.1x6g(x)=-0.5x3

Q: Prove the following statement. ∀c ≥ 1 ∃d ≥ 1 ∀x ≥ d : c ≤ 3x. You may assume that c, d, and x are…

A:

Q: Prove that V2 is irrational.

A: We will prove by the method of contradiction. We will first assume the number to be rational and…

Q: If Ua = {(x1, x2, x3)" E R³|x1+ 2x2 + 3ax3 = a} is closed under addition, then a = 0. Prove that the…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Prove A X (BUC) - (Ax B) U (A x C)

A:

Q: Define sets A and B as: : {n E Z\n = 4r + 3 for some integer r}. • B= {m E Z m = 4s – 1 for some…

A: the objective is to solve the above questions.

Q: Consider the statement: (x + 1)2 (y + 2) is even if and only if x is odd or y is even. Write it in…

A:

Q: 2. Let a, b € Z, where a > b and a 0. Show that there exist integers q and r such that a = bq+r,…

A: Introduction: The well-ordering principle is known to be a basic as well as significant property…

Q: If x and y are real numbers and x>1, prove that there exists a positive integer n such that x" > y

A:

Q: 4. Let R be the set of all real numbers, xER and n E N such that n 2 2. If (1+x) > 0, prove that P,…

A:

Q: If a<b<c<d, then prove that for any real 2,

A:

Q: Translate these statements into English, where R(x) is "x is a rabbit" and H(x) is "x hops" and the…

A:

Q: - Consider the open statements: P(x):x = -2 and Q(x):x² = 4 over the domain S = {-2,0,2}. State each…

A: Since you have posted a multi subparts question according to guildlines I will solve first three…

Q: Prove or disprove the following statement: "For all real numbers x, y, [xy] = [x][y]." (3 marks)

A: Introduction: Two important functions are frequently used in mathematics and computer programming.…

Q: 4. Write an analysis of proof for each proposition below by using construction method. a) If a, b,…

A:

Q: Use the method of direct proof to prove the statement   1.If x is odd, then x2 is odd

A: Let x is any odd integer. The definition of odd integer gives, x=2y+1 Here, y is also integer.…

Q: Let T be the statement Vx E R, 0 < x<1=x-1s 0. 4.1. Write the converse of T. 4.2. Write the…

A:

Q: Suppose x is a real number. Prove that if x 1 then there is a real number y such that y+1 = x. 4-2

A:

Q: Identify the axiom or postulate that applies to the following statement.     If  x = AB + CD + EF +…

A: We have used the axioms here......

Q: Prove the statements: V5 is irrational.e

A:

Q: Prove that if x is a real number, then [2r] = [r] + r+

A: Let us consider x=n+∈     (Because x is a real number) where n is integer part and ∈ is fractional…

Q: 3. Verify that each of the following statements is a false statement by finding a counterexample for…

A: Both statements are false : We can verify by giving an example. In the first statement for x=2 ,…

Q: Suppose f(x)=2.3*x4 and g(x)=−0.4*x3 . Which of the statements is not true?   Group of answer…

A: The functions area given by fx = 2.3x4 gx = -0.4x3 To evaluate: The end-behavior of the function.

Q: Let x e R. Use the method of proof by contraposition to prove hat if x² – 6x + 8 > 0, then x > 4 or…

A:

Q: Suppose that the domain of the propositional function P(x) consists of the integers -2, -1, 0, 1,…

A:

Q: - q)^¬(pq) → ¬(q→ p). Λ -

A: Given clear explanation below

Q: A subset U of the real numbers is open if and only if for every x in U there exists a positive…

A:

Q: Prove that if a and b are integers, with b > 0, then there exist unique integers q and r satisfying…

A: To Prove -  If 'a' and 'b' are integers, with b&gt;0, then there exists unique integers 'q' and 'r'…

Q: b) Prove that A° U B° C (AU B)°. Give an example to show that equality does not always hold.

A: Here weuse the fact  if A is subset of B then A° is subset of B°.

Q: Translate these statements into English, where R(x) is "x is a rabbit" and H(x) is "x hops" and the…

A:

Q: Let A = {n ℤ | n = 5r for some integer r}and B = {m ℤ | m = 20s for some integer s}.Determine which…

A:

Q: For all sets X, Y and Z use the element argument method to prove (X – Y) n (Y – Z) n (Z – X) = 4.

A: let X,Y,Z be any sets  claim- by using element argument method prove that X-Y∩Y-Z∩Z-X=∅

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.