| Line 5: | Line 5: | ||
x∈A implies x∈B | x∈A implies x∈B | ||
| − | Basic Outline of the Proof that A is a subset of B: | + | '''Basic Outline of the Proof that A is a subset of B:''' |
| − | & | + | · Suppose x ∈ A |
| − | 1. Say | + | 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 | ||
| − | & | + | &midbullet Conclude x∈B |
Revision as of 06:46, 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 &midbullet Conclude x∈B
