Let A = {0, {0}, {Ø, {Ø}}}. State whether each of the following statements is true or false: ØCA {0, {Ø}} C A {0, {0, {0}}} € P(A) A – {0} = {0, {0, {Ø}}} |

Q: Let x, y ∈ R and suppose for every ε > 0, we have x ≤ y + ε. Then x ≤ y.

A: Given:  the given statement is false eg.    let x=2, y=1  and ε =2 ≥0         we have y+ε=3 and x=2…

Q: If u (E) =0, then E is measurable.

A:

Q: (a) а aH (b) aH = H if and only if a e H (c) aH = bH or aHn bH = ø (d) aH = bH if and only if a ' b…

A: Let H be a subgroup of G and let a and b belong to GThen the following conditions hold: (a) a∈aH (b)…

Q: If a+a e c(R) for all ae R. then Commutative is prove that

A:

Q: Let A and U = H. Then A2017U is equal to

A: The given matrix is A=-120-1 find A2=-120-1-120-1=1+0-2-201=1-401 therefore A2=1-401 similarly…

Q: Let AB = AC. Prove that if det(A) = 0, then B = C.

A: The given question Let AB = AC. Prove that if det(A) = 0, then B = C. this question is not correct…

Q: Prove: If a > 0, then (1/a) > 0.

A: It is given that a> 0.It is known that if ab > 0 then a > 0 or b > 0 or a< 0 or b…

Q: 2. Answer one of the following questions: (a) Show that a necessary and sufficient condition that…

A:

Q: 2. When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and…

A:

Q: Let X~U (0,0), then P(X > X²) is

A: Given that X~U0,θ fx=1θ-0=1θ, 0≤X≤θ

Q: prove that: DO e de a e +6 2/3 cwhere a, b > o

A: Where a, b>0

Q: If m and n are positive integers and w = g(x"y"), then show that dw dw = my dy

A: Given w=g(xmyn).

Q: Show that 1-r for any r 1 1 and any 3. nEN

A: answer

Q: Let A and Bbe everts satisfying P(A)=04, P(B)-0.6 and P(An B)-01.Find P(A B)

A: P(A) = 0.4 P(B) = 0.6 P(A∩B)=0.1

Q: Let X ~ N(0, 1). For any € > 0, show that P(|X| > c) ≤ ²c - ??

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: Let a and b belong to Q with b ≠ 0. Show that Q(√a) = Q(√b) if and only if there exists some c ∈ Q…

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Q: Let m eN and a, b e Z be such that (a, m) = 1 and (b, m) Let h = 0m(a), k = 0m(b), and let n = 0m…

A:

Q: Let AB = AC. Prove that if det(A) + 0, then B = C.

A: Given: Let AB=AC. To Prove: If detA≠0, then B=C

Q: Let P = {p:p=6x-1, for some x EZ} and Q= {q:6y+5, for some y EZ). Prove that P= Q

A:

Q: Give a natural deduction proof of ¬(3 x)(A(x) A B(x)) → (V x)(A(x) → ¬ B(x)).

A:

Q: Given x > 0 and a real number y, there is an n in N such that nx > y.

A:

Q: Prove the following theorems: 1. If a /b, then a / bc.

A: Suppose that a | b. If a|b, then by definition there exist an integer m such that b=ma. That is,…

Q: If X =Y (hom oemorphic) and Y has a property P then X has the same property P. True False

A:

Q: Let a, b e C. (i) Prove that if |a| <1 and |6| < 1, then a - b < 1. 1- āb

A:

Q: Let a e Z. Prove that if 7 | 2a, then 7 | a.

A:

Q: If a z 0, then |a If a < 0, then |a||

A: if a&gt;=0, |a| = ?  if a&lt;0, |a| = ?

Q: Let a = 8 and b = 9. Find m,n E Z such that am+bn =1.

A:

Q: 2. Prove that any two non-zero elements a, b in a P.I.D. R have a g.c.d. Further if d e R is a…

A:

Q: 69. If a>0, h>0 and ne N, prove that there exists 0, 0<0< 1, such that h? (- 1)" - ' h"- ! 1 1 h (-…

A:

Q: 30 Let A, B E M, and suppose that A² = 0 = B². Show that A and B are unitarily similar if and only…

A: I

Q: If Ea, is divergent and 2b, is divergent, then E(a, + ba) is divergent.

A: Taking an example and than we are trying to understand tha statement.

Q: If x]y then gcd (x, y) = y. إختر واحدا: Las O

A: Given x|y hence y=ax It implies that y is a multiple of x

Q: Prove or disprove: If (xn) and (yn) are subsequences of each other, then xn = yn.

A: Definition: Suppose ann∈ℕ be a sequence. A subsequence of this sequence is a sequence of the form…

Q: p) Prove that if ac | bc and c +0 then a | b.

A:

Q: Prove: For c &gt;= 0 , | a | &lt;= c if and only if -c &lt;= a &lt;= c

A:

Q: Find conditions on a, b, c, and d such that AB = BA

A: , We need to find the values of a, b, c and d such that AB=BA

Q: Find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100.

A: By adding the cubes of positive integers we solve the given problem.

Q: 9. Prove that the following pair of formulas are equivalent in SDE. U → -(E V D), (-E A ¬D) →¬U

A:

Q: 4.2. Let a, b E Z, where a 0 and b 0. Prove that if alb and bla, then a = b or a = -b. -b.

A:

Q: R is commutative if and only if R[x] is Commutative. True or False

A: The given statement is true. If Rx is cummutative.So, R⊂RxRx is cummutative.R is also…

Q: a Let A Show that A is nonsingular if and d only if ad – bc + 0.

A: Known fact: A matrix is said to be invertible (nonsingular) if its determinant is nonzero.

Q: (c) If A E M,(R) is non singular and n 2 2, prove that det(adjA) = (det A)"- (d) If A E M,(R)…

A:

Q: ke an example at a Noe therian m adu le is not Artini an.( Prove)

A:

Q: Prove that if A={- :n EN, then A' ={0}. Hint: (a) if x1, then . (d) if x=0, then x EN.

A: A set A=1n:n∈N then A'=0. i.e. the set of limit point contains only 0 element.

Q: Prove by logical equivalences and rules of inference that vx(L(x)→ R(x)), 3x(P(x)^ ~ R(x))E ~(P(x)→…

A: Rules of inference are the tools to prove logical equivalence. This method of proof excludes…

Q: 4.2. Let a, b € Z, where a + 0 and b + 0. Prove that if alb and bla, then a = b or a = -b.

A:

Q: 2. Let A be non singular. Show that if Ax = 0, then x = 0.

A:

Q: 2. Answer one of the following questions: (a) Show that a necessary and sufficient condition that…

A:

Q: Show that Oa = {a} if and only if a e Z(G).

A: For a∈G, Oa denote the orbit of 'a' under the conjuction action.The orbits under the conjucation…

Q: Let A={x:xER and x is a solution of x²+2=0},then A is a null set ylgn ihi

A: We have to check whether the statement, "Let A=x:x∈R and x is a solution of x2+2=0, then A is a null…

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.