Homework Help

Prove for sets M, N, M-N ⊆ M? ⊆ is the symbol for subset. This is for a discrete...

user profile pic

nikhilnair93 | Student, Undergraduate | eNoter

Posted April 4, 2012 at 4:11 AM via web

dislike 1 like

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! 

Tagged with discrete, discrete math, math, proof

1 Answer | Add Yours

Top Answer

user profile pic

Matthew Fonda | eNotes Employee

Posted April 4, 2012 at 5:21 AM (Answer #1)

dislike 1 like

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.

Proof:

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.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes