Difference between two seemingly similar sentences [duplicate]

Solution 1:

This sort of quibble is often made by people with a mathematical background (like me for example!). English often lacks in precision when discussing such things.

In fact, the difference is usually indicated by context and voice tone rather than grammar.

John: All our friends like cheese. Let's have a cheese party!

Mary: All of our friends don't like cheese. What about Anna? She hates it

John: Oh yes, I'd forgotten.

John: Let's have a cheese party!

Mary: All of our friends don't like cheese. In fact they all hate it..

John: Okay, you decide then.

In mathematics and formal logic, special symbols are used to indicate the difference. Precision is key in these fields.

Note

It is often to my regret that there is no way of showing voice-tone accurately on this site. It can entirely change the meaning of a phrase according to how it is said, e.g. "You're a genius" can be said with admiration or with extreme sarcasm, Only voice tone indicates the difference.