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?