f(1) = E÷ Question 4. Let f be the function defined by the series for all x such that -1

Q: Consider the statement: For any numbers a and b, if a + b is odd, then either a or b is odd. First,…

A: Kindly refer to Step 2 for the solution.

Q: Prove using the properties of set operations: a. A - B and An B are disjoint.

A: Solution-: We want to prove A-B and A∩B are disjoint.

Q: Find the symbolic logic of the sentence and then find its negation. There exists a non-zero real…

A: Given that, There exists a non-zero real number y such that y+ x = x, for every real number x. The…

Q: The Boolean sum of the variables z, y and z or their complements, that has the value 0 if and only…

A: Given x=0y=1z=1 Thus yc = 0zc = 0 We know that  a+b = 0 if and only if both a and b are zero

Q: Select the set that is equivalent to (Cn B) UA. (Cn B)UA (CUB) UA (CnB) nA (CUB) NA

A:

Q: Say True or False and justify your answer. P(A∪B)⊆P(A)∪P(B)

A:

Q: 5. Use proof by cases to prove the statement: If a and b have the same sign, then |a+b| = |a| + |b|.

A: The given problem is to prove the given statement by using the proof the cases. The given statement,…

Q: If a and b are any real numbers, is the statement a * b = b * aalways true? Why or why not?

A: Given that, a and b are any real numbers.   The objective is to decide whether the statement a×b=b×a…

Q: Which of the following is a quantitive variable? A) a persons gender b) the make of washing…

A: We need to use concept of quantitative and qualitative variables to answer this.

Q: a. write the converse of: "if apples are oranges, then 1+3=5."

A: The converse of "if p, then q" is "if q, then p." Here,  p: Apples are oranges q: 1+3=5

Q: i owing expression. a+bi nswer below:

A: Solution  Given  ia+bi

Q: Answer whether it is true or false. a. Is 1 ∈ {1}? b. Is {2} ⊆ {1,{2},{3}}? c. Is {1} ⊆ {1, 2}? d.…

A: # we are entitled to solve three subparts, please resubmit the question with other sub parts if you…

Q: Use propositions to prove that if A ⊆ B and A ⊆ C, then A ⊆ (B ∩ C).

A: .

Q: Let S(x,y) be the predicate "person x has spoken to person y," where the domain for the variables x…

A: We know that:

Q: Prove or disprove: For all sets A, B, we must have 24A2(AAB) = 2B.

A: Given, 2A∆2A∆B

Q: Simplify the given expression. Cite a property from each expression     A − (A ∩ B)   ∩ B − (A ∩…

A: We simplify the given expression.We state  property from each expression.

Q: Minimize the following Boolean expression: - e) POR + POR+ P Q R+PQR+P Q R+PQR

A: The given expression is PQR+PQR+PQR+PQR+PQR+PQR Use the formula A+A=1…

Q: Prove. all sets A,B and C, (a) (A-B)- C = CA-C)-B disprove each of the following for or

A: We Know that A - B means elements of A which are not the elements of B. i.e.      A - B = {x : x ∈ A…

Q: Give the dual of the Boolean statement: A + (B ∙ 0) = A ∙ 1

A: Given, The Boolean statement: A + (B ∙ 0) = A ∙ 1

Q: Sn : n(n + 1)(2n + 1) :2 %3D 6. i= a) Statement S6: b) Statement S5 : || +

A:

Q: Q9A. Give the value for the Boolean expression. Use the following values for the variables when…

A: Given- The expression: xyzw To find- The value of the given Boolean expression when x = 1, y = 1, w…

Q: AV B ¬A→ (CAD) AV¬B ¬AV ¬(С V D) Find the value of all variables that are solvable

A:

Q: Which of the following arguments is not valid Select one: A. S-r B. p9 SV 9 C. SV . D. SVq

A: Given: Determine the following arguments are valid or not, A)         p→q         s→r        s v…

Q: Which of the following statements are true? I: If ACB, then AC conv B. II: If AC B, then conv A C…

A: Option (C) is correct

Q: Disprove: For all sets A, B, C, and D, (AUC) × (BUD) C (A × B) U (C × D).

A:

Q: Which of the following is logically equivalent to PV-P? OPP OPP OPA-P ОР0-Р

A:

Q: Are (p A g) and vp A ng logically equivalent?

A:

Q: For all real numbers a and b, |a+b| = |a| + |b|.

A: This question is about discrete maths.

Q: Translate the following sentences into symbolic logic There exists a real number a for which a+x=x…

A: Symbolic logic : The logical statement in which the symbols used to denote propositions, terms, and…

Q: Draw the logic diagram for this expression: (p v q) ^ (!r v !q)

A: The logic diagram is an equivalent diagram of a Boolean expression, which is represented using the…

Q: Write a negation for the following statement: For all real numbers x, if x (x – 2) > 0, then x > 2…

A:

Q: Let A = 1 1 1`1 1 1 1], B= CD c=H₁ 1 1 Which of the following expressions is NOT defined?

A: we need to find which of the given expressions is not defined.

Q: Find P(AorB) if P(A)=0.3, P(B)=0.5 and A and B are independent

A: P(A) = 0.3 P(B) = 0.5

Q: Fill out the following expression with logical operators so that it returns False as the answer. You…

A: Equalities and inequalities

Q: 3. Write the contrapositive of: VaeZ, if 6|a then 2| a and 3| a

A: The given statement is, ∀a∈ℤ, if 6a then 2a and 3a The objective is to write the contrapositive of…