Prove for sets M, N, M-N ⊆ M? ⊆ is the symbol for subset. This is for a discrete math class. I'm trying to prepare for a test about proofs, so any help would be appreciated! 

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Matthew Fonda eNotes educator| Certified Educator

For this problem, a direct proof is the way to go. Start by defining set difference and subsets, then use these definitions to reach the conclusion.

Set difference: `A-B = {x \in A | x \notin B}`

Subset: A is a subset of B if every element of A is also an element of B.


Let M, N be sets.

Let `x \in M-N` . By definition of set difference, it follows that `x \in M` . This shows every element in M-N is also in N, and therefore M-N is a subset of M.

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