| Line 4: | Line 4: | ||
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 | + | '''·''' Suppose x ∈ A |
| − | 1. Say what it means for x to be in A | + | |
| − | 2. Mathematical details | + | 1. Say what it means for x to be in A; |
| − | 3. Conclude that x satisfies what it means to be in B | + | 2. Mathematical details; |
| − | + | 3. Conclude that x satisfies what it means to be in B; | |
| + | |||
| + | '''·''' Conclude x∈B | ||
Revision as of 06:47, 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
