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Function: driver
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Function: require_once
수학동아 - 폴리매스
함께 풀고 싶은 문제
나도 수학쌤 문장제 문제를 변형해 문제를 내는 곳입니다.
△π
2021.02.25 03:14
조회 488
집합과 연산에 대한 군이라고 하면, 다음과 같은 조건을 성립하면 만족한다.
1)그 연산이 그 집합에 대해서 닫혀있다.
2)그 연산에 대해 결합법칙이 성립한다.
3)항등원이 존재한다.
4)그 집합에 속한 원소 x에 대해 역원 x'이 존재한다.
항등원이란, 그 집합에 속하는 원소 a에 대해서 연산을 *라 하고, 다른 원소를 e라 하면
a*e=e*a=a를 만족하면 e는 항등원이다.
역원이란, 그 집합에 속하는 원소 a에 대해서 다른 원소를 a'이라 하면
a*a'=a'*a=e를 만족하는 a'을 a의 역원이라고 한다.
(1)다음과 같은 조건을 만족하는 집합 G와 연산 *이 있다.
1)*은 G에 대해서 닫혀있고, 결합법칙이 성립한다.
2)G의 원소인 a에 대해 e*a=a가 성립하는 G의 원소 e가 항상 존재한다.
3)G의 원소인 x에 대해 x'*x가 성립하는 G의 원소 a'이 항상 존재한다.
이 때, (G,*)이 군임을 증명하시오.
(2)다음과 같은 조건을 만족하는 집합 G와 연산 *이 있다.
1)*은 G에 대해서 닫혀있고, 결합법칙이 성립한다.
2)G에 속하는 임의의 원소 a,b에 대해 x*a=a*y=b가 성립하는 x,y가 항상 존재한다.
이 때, (G,*)이 군임을 증명하시오.
지금 바로
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