How to convert an English sentence that contains "Exactly two" or "Atleast two" into predicate calculus sentence?
For example: There are two people with income less than 4K/year.
[Math] How to convert an English sentence that contains “Exactly two” or “Atleast two” into predicate calculus sentence
logic
Best Answer
"There are at least two objects satisfying P" can be expressed in first-order logic as $$\exists x \exists y (x \neq y \wedge P(x) \wedge P(y))$$
"There are exactly two objects satisfying P" can be dealt with by first rephrasing to "There are at least two objects satisfying P, but there are not at least three objects satisfying P" and using the above idea, or alternatively as $$\exists x \exists y ((x \neq y \wedge P(x) \wedge P(y)) \wedge \forall z (P(z) \rightarrow (z=x \vee z=y)))$$