HW3] Write the first 12 terms of {sin()jeN§ Find the liminf and the lim sup the details as a boue. showing Find the limits of the subseguences: lim x, lim X 4k+ kaa 4k+2 lim Xyk lim X *4k+3 Which agree with the limsup and liminf ?

Q: U = {x: x is first ten positive integers} A = (1, 2, 5, 6, 9, 10} B=(2, 4, 6, 8, 10} C = (3, 4, 7,…

A: Here A-B =the set of all those elements which are in A but not in B             i.e A-B={1,5,9} And…

Q: Write a proof that proves the Union Un an element of natural numbers (-1/n, 2-1/n)=(-1, 2). Also…

A: The given interval is (-1/n,2-1/n) where natural number n belongs to positive integers. So that we…

Q: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: Let J={1,2,3,…}, the set of counting numbers and let R be the set of real numbers. Is R-J countable?…

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Q: help please use the contraposition to prove if x+ y < 10,  then x< 5 or  y< 5.

A: Step 1: Step 2: Step 3: Step 4:

Q: List the first four elements of the set { x | x = 4k + 1, and k is a natural number}  (List each…

A: Given set { x | x = 4k + 1, and k is a natural number} = {4×1+1, 4×2+1, 4×3+1, 4×4+1, ... } = {5, 9,…

Q: Let a,b,c,d be real number with a < b < c < d. Express the set [a,b] U [c,d] as the difference of…

A: We have given that, a, b, c, d are real numbers with a &lt; b &lt; c &lt; d. We need to express a, b…

Q: Prove that if a,b belong R(Real Numbers) then |a|-|b| is lesser or equals to |a-b|

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Q: Prove that la + b + c| < ]a] + ]b| + |c[

A: Prove that,    a+b+c≤a+b+c

Q: Insert "⊆" or "⊈" in the blank to make the statement true.{4, 6, 8}     {3, 4, 5, 6, 8}

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Q: Show that if a and b are real numbers and a!=0 then there is unique number r such that ar+b=0

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Q: Prove the following in axiomatic system. (A- (-B - C),~B}-A-C

A: Laws of inference are very useful in proving mathematical statements. We can build a sequence of…

Q: Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9), A = {1, 2, 3, 8}, and B = {1, 2, 3}. Find the set An B. AnB =…

A: U={1, 2,3,4,5,6,7,8,9}A={1, 2,3,8}B={1, 2,3}

Q: UA_n is open where A_n=(n-1,n).

A:

Q: Write the set of ordered pairs as a mappi 2) {(-5, 5), (-4, 1), (0, 1), (3, 1), (5, 4)}

A: Given: ordered pairs:  {(-5, 5), (-4, 1), (0, 1), (3, 1), (5, 4)}…

Q: sing direct proof, prove the following statements: 1. Prove: If x2-4=0, then x = 2 or x = -2. 2. If…

A: follow next step

Q: "

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Q: use set identities and membership table to prove that (A-B)-(B-C)=A-B solve

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Q: {5}⊂{1, 3, 5, 7, 9,...} true or false

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Q: If a statement is false, explain why. {1, 8, 6, r} = {6, r, 1, 8}

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Q: Define Conjugate transpose.

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Q: Determine whether following is true or false. All creatures die. All human being are creatures.…

A: The given problem is a problem of propositional logic .  In the given problem there are two…

Q: If then and ui

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Q: How many pairs of ordered numbers exist such that sum , product and quotient are the same?

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Q: 7- Consider the universal set U = {1, 2, 3, ..., 8, 9} and sets A = {1, 2, 5, 6}, B = {2, 5, 7}, C=…

A: A∩B represents common elements in A and B. Given that A=1,2,5,6 and B=2,5,7 A∩B=2,5

Q: Find the dual of the statement (xy¯¯¯)+(x¯¯¯z)

A: To find the dual of statement , we replace • by + and + by •

Q: Let a and b be two positive real numbers. Let p > 1 and q> 1 be such that + = 1 (q is called the…

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Q: When can a theorem be cited as a “reason" for a proof?

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Q: provide a recursive definition for the set Y of all negative multiples of 7.

A: Consider the provided question, Recursive definition: Recursion is the general definition term for…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.