Introduction

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Subsection 4.3.1 Introduction

Predicate logic, like Boolean logic, is useful because it gives us a way to represent things we care about and then to reason about them. We’ve already seen a lot of examples in which we have translated back and forth between English and logic.

Prime(269) 269 is a prime number.

$\forall $ x (Bear(x) $\rightarrow $ HasTail(x)) All bears have tails.

CurrentProjectOf(Shazaam, Chris) Shazaam is a current project of Chris.

$\forall $ x (Pen(x) $\rightarrow $ $\exists $y (ColorOf(y, x))) Every pen has a color.

$\forall $ P ($\forall $ x, y ((x = y $\wedge $ P(x)) $\rightarrow $ P(y))) If x and y are equal, they share all properties.

In this section, we’ll practice that translation skill a bit more before we move on to see how we can actually construct proofs with the statements that we’ve made.

Then we’ll return to this issue after we’ve seen how to construct proofs using the statements that we write.