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 \(b\) and \(c\) are variables which represent non-negative integers.

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

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

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

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


These symbols have the following meanings:

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

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