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
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
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 9E: 9. The definition of an even integer was stated in Section 1.2. Prove or disprove that the set of...
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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.
(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
Transcribed Image Text:/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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