The set {1, 2, 4, 7, 8, 11, 13, 14} is a group under multiplication modulo 15.…
2005
The set {1, 2, 4, 7, 8, 11, 13, 14} is a group under multiplication modulo 15. The inverses of 4 and 7 are respectively
- A.
3 and 13
- B.
2 and 11
- C.
4 and 13
- D.
8 and 14
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Correct answer: C
Solution: Find inverses in the group by checking which element multiplies to 1 modulo 15.
For 4: 4 × 4 = 16 ≡ 1 (mod 15), so the inverse of 4 is 4.
For 7: 7 × 13 = 91 ≡ 1 (mod 15), so the inverse of 7 is 13.
Both inverses (4 and 13) are elements of the given set {1, 2, 4, 7, 8, 11, 13, 14}.
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