| Line 10: | Line 10: | ||
'''·''' Suppose x ∈ A | '''·''' Suppose x ∈ A | ||
| − | 1. Say what it means for x to be in A | + | |1. Say what it means for x to be in A |
| − | 2. Mathematical details | + | |2. Mathematical details |
| − | 3. Conclude that x satisfies what it means to be in B | + | |3. Conclude that x satisfies what it means to be in B |
| + | |||
'''·''' Conclude x∈B | '''·''' Conclude x∈B | ||
Revision as of 06:48, 25 November 2012
Proving one set is a subset of another set
Given sets A and B we say that is is a subset of B if every element of A is also an element of B, that is,
x∈A implies x∈B
Basic Outline of the Proof that A is a subset of B:
· Suppose x ∈ A
|1. Say what it means for x to be in A |2. Mathematical details |3. Conclude that x satisfies what it means to be in B
· Conclude x∈B
