| Line 10: | Line 10: | ||
'''·''' Suppose x ∈ A | '''·''' 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 | '''·''' Conclude x∈B | ||
Revision as of 07:48, 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
