Hello jokke22You can do this in two ways: Either re-write it as 'It is not true that if x shines, then x is a diamond'; or as 'There exists an x, x shines and x is not a diamond'

The first gives you:

and the second:

Either of these is equally correct.

Re-write this as 'There exists an x, such that for all y, if y is a diamond then x likes y'2. Someone likes diamonds

So this symbolises as:

This can be re-written 'If x is a diamond, and y likes x then if z shines, then y likes z'. I'll start you off:3. Everyone who likes diamonds likes everything that shines

Can you finish it?

Re-write this as 'There exists an x, such that if x likes y, then y shines'4. Someone likes only thing that shines

This is 'There exists an x, such that if y shines, then x likes y.'5. Everything that shines are liked by someone

'There exists an x, such that x is not a diamond and x does not shine and for all y, y likes x.'6. There is something that is neither diamond or shines, but are liked by everyone

Can you complete these now?

Grandad