The correct relationship between α and β for a given transistor is:

Relation between α and β:

The common-emitter current gain (β) is the ratio of the transistor's collector current to the transistor's base current, i.e.

And the common base DC current gain (α) is a ratio of the transistor's collector current to the transistor's emitter current, i.e.

The transistor currents are related by the relation:

IE = IB + IC

α can now be written as:

Dividing both the numerator and denominator by IB, we get:

Since 

 'or'