# Simplifying SOP: implementing OR with NAND

I am learning how to implement basic logic gates using NAND. I have learnt that you can use De Morgan’s theorem as such:

$$a+b = \bar{\bar a} + \bar{\bar b} = \overline{(\bar a *\bar b)}$$

In other words, we would need two NOT gates (which are basically NAND gates), and another NAND gate.

However, I want to practise Boolean algebra simplification. Using a truth table I have formed the Sum of Products:

$$f(a,b)=ab’ + a’b + ab$$

I have worked down a number of paths unsuccessfully. I would appreciate if someone could either show the steps of simplification, or give me some guidance on the laws to use to achieve this simplification. If there are any notation mistakes I have made, please let me know 🙂