The lengths of a triangle's sides a, b, c must satisfy c<a+b, a<b+c, b<c+a,and this is also a sufficient condition.
The first: 14<7+8, 7<8+14 and 8<7+14 are all true. YES
The second: 10<3+7 is false. NO
The third: 14<6+7 is false. NO
The fourth: 10<4+6 is false. NO
The answer: the first set only.
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