Kenneth h rosen Q29. Chapter 1 section 1.3 Predicate logic

Question

Can anyone explain from for all y??. I am not getting that part how for all is added and implied x=y.

 

Answer 1

Here, ∃xP(x) means there exists at least one x such that P(x).

Now observe the phrase – “one of your tools”. It means that only one tool is not at the correct place but in excellent condition. To ensure that only one tool is not in the correct place, we are removing the possibility of having more than one tool being in the correct place but in excellent condition.

The statement following “ for all y….” ensures that if ever we find another tool such that !C(x) and E(x), it means that the tool must be the tool x. In simple words, no other tool except x is present such that !C(x) and E(x).

 

I hope you got the intuition.

~NJ~