GCSE Logic >Algebra< Gates Latch NAND Array Schmitt NOT Truth Tables 
Logic Algebra 

If you have a good understanding of the logic gate rules, it is possible to work out a simpler solution just by examining the truth table and thinking hard. But this is a rather hit and miss approach and Karnaugh maps and Boolean algebra can be faster and more reliable methods but neither is easy.
Boolean algebra can be used to simplify expressions/circuits to generate a more optimal solution.
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