Computers rely upon strict interpretations of logical statements. Can you think like a computer, and identify the statement below that is false?
Assume that b and c are variables which represent non-negative integers.
A) ¬∀c:∃b:(2b=c)
B) ∀c:∃b:¬(2b=c)
C) ¬∃b:∀c(2b=c)
D) ∀c:¬∃b:(2b=c)
Note:
These symbols have the following meanings:
- ∀x is the universal quantifier, which asserts truth for every possible value of x within its scope. It can be read as "for all x".
- ∃x is the existential quantifer, which asserts truth for at least one value of x within its scope. It can be read as "there exists x".
- ¬x is the negation symbol. It can be read as "not x".