Let x, y E N, determine each of following statemen is true or false (N means Natural number, natural number starts with 1 and O is not counted as a natural number.)

Q: Complete this formal proof of-(~A&-B) from A in as few lines as possible. Justify subproof…

A: The objective is to complete the proof of

Q: (1) *, Let A and B be sets prove the following. (c) A C B if and only if B° C A°.

A: Let A and B be sets.

Q: 7. Show that if A and B are similar, then det A = det B. %3D

A:

Q: Assume that A and B are in NP. Show A n B that is also in NP.

A:

Q: Given that U = all students at a university, D = = graduate students. Let |U| = Your Registration…

A: To determine number of evening graduate CS majors by illustration through venn diagram. U= all…

Q: If a,b,c,d are in continued properties,prove that

A:

Q: If "C, = K "C,, then K is n-1 %3D

A: Combination problem....

Q: Let S = {10n – 1: n e Z}, T be the set of odd integers, and U Prove that S CTNU. {5т + 4: т E Z}.…

A: Consider the given information. Here, S=10n-1:n∈Z And, U=5m+4:m∈Z And, the set T is the set of odd…

Q: 4. Is the set Q² x {a,b,c} countable or uncountable? You must justify your answer with a proof.

A: Given : ℚ2×a , b ,c  To Prove : ℚ2×a , b ,c  countable or uncountable

Q: Find a pair of numbers that provides a counterexample to show that the given statement is false.…

A: We know that, The product of two even counting numbers is an even counting number. The product of an…

Q: If D =diag(λ1,λ2,...,λn), show that for every positive integer k, Dk =diag(λk 1,λk 2,...,λk n).

A:

Q: Show that for all n, m∈Z if n+m is even, then either n and m are both even or n and m are both odd.

A: Use the results of addition of integers.

Q: 14)If the numbers On are and an= 3an defined by a= I , --20- for nz3, faoce that

A: We will first write the given recurrence relation  in homogeneous form then find its characteristic…

Q: Create a Venn diagram on first impressions at school, at work, and at both school and work. What do…

A: Create a Venn diagram on first impression at school, at work, and at both school and work. What do…

Q: Let A, B and C be sets such that Al = 17 |B= 10 C= 11 and the intersection of any two of these sets…

A:

Q: a. Used by competitors o. That does not currently exist in a organized form :. That already exists…

A: Secondary data is known as the data that are collected through public sources, i.e., census,…

Q: [0,1] is not countabe. صواب İhi O

A: True

Q: If m, n, p, q are integers, n > 0, q > 0, and r = m/n = p/q, prove that

A:

Q: Draw a Venn diagram so that N(U) = 15, n(S) = 10, n(T)= 4, n(SUT) = 13

A: We will use the formula: To find the number of elements which are in both S and T

Q: (a) In(ax), (b) In(x* + 1), (c) æ In a, (d) æ", (e) In(e" + 1), (f) exp(e" +1), (8) In +1

A: We have to differentiate the given functions.

Q: Show that the Post Correspondence Problem is decidable over the unary alphabet S = {1}.

A: To Prove :- The Post Correspondence Problem is decidable over the unary alphabet S =1.

Q: 3. Suppose a, b, c E Z. Prove that if a? + b = c²,, then a is even or b is even.

A:

Q: O Ho: H Diff = 0; H, H O Ho: H Diff = 0; H, H Diff >0 O Ho: Holder =H Youngeri Hai Holder>HYounger O…

A: Given : An equestrian enthusiast is interested in the racing times of horses. She believes an older…

Q: 1. Let x, y, z be integers. Prove that if x(y + z) is odd, then x is odd and at least one of y or z…

A:

Q: Let S = {(x, y) E R X R: y - x = integer} List of four members of [-3]

A: GivenS=x,y∈IR×IR: y-x=Integernow-3=x∈IR: -3-x=Integernow, 1∈IR,2∈IR , 3∈IR and 4∈IRso the four…

Q: Let c= and D= [7 -1 -2]. 1 - 6 Find CD if it is defined. Other.se, tap on "Undefined". CD = [00)

A: The given matrices are C=04-6 and D=7-1-2

Q: If sets X union Y are countable, then prove or disprove that both X and Y are countable.

A:

Q: Given that U = {x : 1 ≤ x ≤ 10, x is an integer}, G = {x : x is a prime number}, H = {x : x is an…

A: Given that U = {x : 1 ≤ x ≤ 10, x is an integer},G = {x : x is a prime number},H = {x : x is an even…

Q: Let the numbers c1, C2, ... be defined inductively as follows: c1 = 0 and for every n >1 the number…

A:

Q: let pcoc) =e" Since). oc G C-},3)

A: The given function is Fx=exsinx, where x∈-π2,π2.  If f'(x)>0 at each point in an interval I, then…

Q: Give a direct proof of the claim: Vn E N, if the last two digits of n are divisible by 4 then n is…

A:

Q: Let d, a, b E N. Prove that

A: Given,  d, a, b∈ℕ To prove that if d|a+b2  and   d|a-b2, then d|b.

Q: Suppose that X, Y are subset of U. If Pr(X)= 0.35, Pr(Y)= 0.36, and Pr (X intersect Y)= 0.09, what…

A: Given Suppose that X, Y are subset of U. If Pr(X)= 0.35, Pr(Y)= 0.36, and Pr (X intersect Y)= 0.09

Q: Hae sets cen lee espected to be free frem many depectice goute consignmet of Lopoo seti

A: Here Given  Wireless Set are manufactured with 25 Joints each  And Probability of Defective…

Q: Let A = {a, a, b, c} and B = {a, b, c}. Prove that A = B. Thus, the number of times an element is…

A: Given A={a,a,b,c} and B={a,b,c} we  have to show that A=B, for  this we will show that A⊂B and B⊂A…

Q: 1. Given a deck of 30 cards labelled with numbers 1- 10 (with 3 cards of each number), how many…

A: From the given information,  A deck of 30 cards labelled with numbers 1-10 (with 3 cards of each…

Q: The set [0,]is (open in [0,1 .A O open in R.BO (not open in [0,1.C O none of above.D O

A:

Q: Let Select one: O 3 0 - A = where k is a real number. Then A is singular if and only if k equals 3…

A:

Q: Is it true that, if S is a nonempty set of positive real numbers, then 0<=inf S?

A:

Q: If dfbetween=3, and dfwithin=60, if alph is set at .05, then Fcrit=?

A: Given, dfbetween=3 dfwithin=60 Significance level (α) =0.05

Q: Let A = {a,b, c} and B = {b, c, a}. Prove that A = B. Thus, the order %3| in which the elements are…

A: The given sets are A={a,b,c} and B={b,c,a}we have to show that A=BResult : two sets A and B are…

Q: If A = {x E N x is odd, x <,7pw many SUBSETS of Acontain no even numbers?

A: If a set contains ‘n’ elements, then the number of subsets of the set is 2n.

Q: (c) Show that the set {r EN | x² % 4 = 1} is equal to the set {EN | x² % 8 = 1}.

A: Two sets are said to be equal if the number of elements in both the sets are equal. Now, we have one…

Q: Given that Z - N(O, 1) use tables to evaluate correct to three decimal places then P(1.24 < Z <…

A: Required probability is P(1.24&lt;Z&lt;2.36)

Q: Assume there are 3500 undergraduate students studying at AUA, 1800 students have taken Business Math…

A: It is an important part of statistics. It is widely used.

Q: det A = 9214녀 Nor4 N 5 O o 2NN

A:

Q: if m is even and n is odd demonstrate that m*n= is even

A:

Q: Let A= then det(3A") = %3D O 18

A: We use Matrix and determinant concept here.

Q: What is the Venn diagram if: U = {x:x is a natural number less than 20} A = {y:y is an odd number…

A: Given: U = {x:x is a natural number less than 20}. A = {y:y is an odd number less than 20}. B =…