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In the group {1, 2, .........16} under the operation of multiplication modulo 17, the order of the element 3 is
- a)4
- b)12
- c)16
- d)8
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In the group {1, 2, .........16} under the operation of multiplication...
Here C1 = {1, 2, -----16} is group under the operation of multiplication moduo 17
So 34 = 81 = 13 (mod 17)
38 = 16(mod 17)
312 = 4(mod 17)
316 = 1 (mod 17)
⇒ order of the element 3 is 16
∴ 0(3) = 16
So 34 = 81 = 13 (mod 17)
38 = 16(mod 17)
312 = 4(mod 17)
316 = 1 (mod 17)
⇒ order of the element 3 is 16
∴ 0(3) = 16
Most Upvoted Answer
In the group {1, 2, .........16} under the operation of multiplication...
Answer:
To find the order of an element in a group under a certain operation, we need to determine the smallest positive integer 'n' such that the element raised to the power of 'n' gives the identity element of the group. In this case, the identity element is 1.
Step 1: Multiplication Table
First, let's create a multiplication table for the group {1, 2, ..., 16} under the operation of multiplication modulo 17.
```
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
--------------------------------------------------------
1 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 | 2 4 6 8 10 12 14 16 1 3 5 7 9 11 13 15
3 | 3 6 9 12 15 1 4 7 10 13 16 2 5 8 11 14
4 | 4 8 12 16 3 7 11 15 2 6 10 14 1 5 9 13
5 | 5 10 15 3 8 13 1 6 11 16 4 9 14 2 7 12
6 | 6 12 1 7 13 2 8 14 3 9 15 4 10 16 5 11
7 | 7 14 4 11 1 8 15 5 12 2 9 16 6 13 3 10
8 | 8 16 7 15 6 14 5 13 4 12 3 11 2 10 1 9
9 | 9 1 10 2 11 3 12 4 13 5 14 6 15 7 16 8
10 | 10 3 13 6 16 9 2 12 5 15 8 1 11 4 14 7
11 | 11 5 16 10 4 15 9 3 14 8 2 13 7 1 12 6
12 | 12 7 2 14 9 4 16 11 6 1 13 8 3 15 10 5
13 |
To find the order of an element in a group under a certain operation, we need to determine the smallest positive integer 'n' such that the element raised to the power of 'n' gives the identity element of the group. In this case, the identity element is 1.
Step 1: Multiplication Table
First, let's create a multiplication table for the group {1, 2, ..., 16} under the operation of multiplication modulo 17.
```
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
--------------------------------------------------------
1 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2 | 2 4 6 8 10 12 14 16 1 3 5 7 9 11 13 15
3 | 3 6 9 12 15 1 4 7 10 13 16 2 5 8 11 14
4 | 4 8 12 16 3 7 11 15 2 6 10 14 1 5 9 13
5 | 5 10 15 3 8 13 1 6 11 16 4 9 14 2 7 12
6 | 6 12 1 7 13 2 8 14 3 9 15 4 10 16 5 11
7 | 7 14 4 11 1 8 15 5 12 2 9 16 6 13 3 10
8 | 8 16 7 15 6 14 5 13 4 12 3 11 2 10 1 9
9 | 9 1 10 2 11 3 12 4 13 5 14 6 15 7 16 8
10 | 10 3 13 6 16 9 2 12 5 15 8 1 11 4 14 7
11 | 11 5 16 10 4 15 9 3 14 8 2 13 7 1 12 6
12 | 12 7 2 14 9 4 16 11 6 1 13 8 3 15 10 5
13 |
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In the group {1, 2, .........16} under the operation of multiplication...
Kaise yoga 16 batyo muje
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In the group {1, 2, .........16} under the operation of multiplication modulo 17, the order of the element 3 isa)4b)12c)16d)8Correct answer is option 'C'. Can you explain this answer?
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In the group {1, 2, .........16} under the operation of multiplication modulo 17, the order of the element 3 isa)4b)12c)16d)8Correct answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about In the group {1, 2, .........16} under the operation of multiplication modulo 17, the order of the element 3 isa)4b)12c)16d)8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the group {1, 2, .........16} under the operation of multiplication modulo 17, the order of the element 3 isa)4b)12c)16d)8Correct answer is option 'C'. Can you explain this answer?.
In the group {1, 2, .........16} under the operation of multiplication modulo 17, the order of the element 3 isa)4b)12c)16d)8Correct answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about In the group {1, 2, .........16} under the operation of multiplication modulo 17, the order of the element 3 isa)4b)12c)16d)8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the group {1, 2, .........16} under the operation of multiplication modulo 17, the order of the element 3 isa)4b)12c)16d)8Correct answer is option 'C'. Can you explain this answer?.
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