Consider the following one-to-one correspondence between the set B of all odd integers and the set N of all natural numbers:N = {1, 2, 3, 4, 5, . . .}B = {1, −1, 3, −3, 5, . . .where an even natural number n corresponds to the negative odd integer 1 − n and an odd natural number n corresponds to the odd integer n.(a) Find the element of B that corresponds to 345 ∈ N.(b) Find the element of N that corresponds to 241 ∈ B.(c) Find the element of N that corresponds to −759 ∈ B.(d) Find the element of B that corresponds to the element 2n ∈ N (for example, −1 corresponds to 2 × 1 = 2,−3 corresponds to 2 × 2 = 4,...)(e) Find the element of B that corresponds to the element 2n + 1 ∈ N /201. Consider the following one to one correspondence between the set B of all odd integers and the set Nof all natural numbers:N - {1,2,3,4, 5, ...}B - {1, -1,3,-3, 5, ...}where an even natural number n corresponds to the negative odd integer 1– n and an odd natural number ncorresponds to the odd integer n.(a) Find the element of B that corresponds to 345 € N.(b) Find the element of N that corresponds to 241 € B.(c) Find the element of N that corresponds to –759 E B.(d) Find the element of B that corresponds to the element 2n EN (for example, -1 corresponds to 2 x 1= 2,-3 corresponds to 2 x 2 = 4,..)(e) Find the element of B that corresponds to the element 2n +1€N

Given: ℕ=1, 2, 3, 4, 5, .... and B=1, -1, 3, -3, 5, .... An even natural number n corresponds to…

Answered: Consider the following one-to-one…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the following one-to-one correspondence between the set B of all odd integers and the set N of all natural numbers:
N = {1, 2, 3, 4, 5, . . .}

B = {1, −1, 3, −3, 5, . . .

where an even natural number n corresponds to the negative odd integer 1 − n and an odd natural number n corresponds to the odd integer n.

(a) Find the element of B that corresponds to 345 ∈ N.

(b) Find the element of N that corresponds to 241 ∈ B.

(d) Find the element of B that corresponds to the element 2n ∈ N (for example, −1 corresponds to 2 × 1 = 2,
−3 corresponds to 2 × 2 = 4,...)

(e) Find the element of B that corresponds to the element 2n + 1 ∈ N

/201. Consider the following one to one correspondence between the set B of all odd integers and the set N
of all natural numbers:
N - {1,
2,
3,
4, 5, ...}
B - {1, -1,
3,
-3, 5, ...}
where an even natural number n corresponds to the negative odd integer 1– n and an odd natural number n
corresponds to the odd integer n.
(a) Find the element of B that corresponds to 345 € N.
(b) Find the element of N that corresponds to 241 € B.
(c) Find the element of N that corresponds to –759 E B.
(d) Find the element of B that corresponds to the element 2n EN (for example, -1 corresponds to 2 x 1= 2,
-3 corresponds to 2 x 2 = 4,..)
(e) Find the element of B that corresponds to the element 2n +1€N

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