Can You Think Like A Computer?

Logic Level 3

Computers rely upon strict interpretations of logical statements. Can you think like a computer, and identify the statement below that is false?

Assume that bb and cc are variables which represent non-negative integers.

A) ¬c:b:(2b=c) \neg \forall c:\exists b:(2b = c)

B) c:b:¬(2b=c) \forall c : \exists b : \neg (2b = c )

C) ¬b:c(2b=c) \neg \exists b: \forall c (2b=c)

D) c:¬b:(2b=c) \forall c : \neg \exists b: (2b = c)

Note:

These symbols have the following meanings:

  • x \forall x is the universal quantifier, which asserts truth for every possible value of xx within its scope. It can be read as "for all xx".
  • x \exists x is the existential quantifer, which asserts truth for at least one value of x x within its scope. It can be read as "there exists xx".
  • ¬x \neg x is the negation symbol. It can be read as "not xx".
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