- #1
skullers_ab
- 16
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Homework Statement
Prove that for every set S, S [tex]\subseteq[/tex] S. Use 'proof by cases'.
Homework Equations
A [tex]\subseteq[/tex] B iff {X: X [tex]\in[/tex] A --> X [tex]\in[/tex] B}
The Attempt at a Solution
I know that A is a subset of B if every element of A is also an element of B. In the case of S [tex]\subseteq[/tex] S, all I can figure out, simply, is:
For every element x in set S, x is an element of S, therefore, S [tex]\subseteq[/tex] S
I do not know how to express this proof in terms of 'cases'. Any help would be appreciated.