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Does a min-weight edge on every cycle

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Question - Is there anybody who knows how to do this problem? This is part of a homework assignment that I am working on and I really need help! Here's how it works:

Consider that a graph has distinct edge weights. Does its lightest edge have to belong to the MST (Minimum Spanning Tree)?

Will its heaviest edge belong to the MST? Does a min-weight edge on every cycle have to belong to the MST?

Prove your answer to each question or provide a counterexample. Your proofs do not need to be excessively formal. A convincing argument is adequate. Is there anybody who knows how to do this?

Reference no: EM13713885

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