- #1
SamitC
- 36
- 0
The problem statement:
Suppose P(x). And if I want to write "For exactly one x, P(x) then:
If we write ∃x [P(x) ∧ ∀y {P(y) → x = y}]. This is as per answer in the books.
Now, suppose P(y) is false. It will still mean x = y.
Shouldn't it be ∃x [P(x) ∧ ∀y {P(y) ↔ x = y}]
Same problem with ∃x [P(x) ∧ ∀y {x ≠ y → ¬ P(y)}]
Thanks
Suppose P(x). And if I want to write "For exactly one x, P(x) then:
If we write ∃x [P(x) ∧ ∀y {P(y) → x = y}]. This is as per answer in the books.
Now, suppose P(y) is false. It will still mean x = y.
Shouldn't it be ∃x [P(x) ∧ ∀y {P(y) ↔ x = y}]
Same problem with ∃x [P(x) ∧ ∀y {x ≠ y → ¬ P(y)}]
Thanks