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A good way to start these problems is by experimenting with logic gate combinations.

Start by looking at ways to link up two NAND gates using either 1 or 2 input switches.

You will clearly need to understand how the target output gates AND, OR, NOT etc. work before attempting this problem!

The sort of thinking used in this problem is typically formally found in Decision Mathematics Modules, but can be attempted with only a simple knowledge of logic gates and truth tables.