Question

Translate each of the following sentences into symbolic logic. I don't eat anything that has a face.

Short answer

The translation into symbolic logic of 'I don't eat anything that has a face.' is \(\forall x, F(x) \rightarrow \neg E(x)\). This states that for every \(x\), if \(x\) has a face, then I do not eat \(x\).

Step-by-step solution

Define symbols

Create two symbols in order to represent the two propositions in the statement: \(E(x)\) to represent 'I eat \(x\)' and \(F(x)\) to represent '\(x\) has a face'.

Write the objects

The objects of consideration should be introduced into the equations. These can be any objects that could potentially have faces, such as animals or fruits. For the purposes of this problem, these objects are not explicitly defined.

Formulate the first draft

The first draft of the translation into symbolic logic would be \(\forall x, (E(x) \rightarrow F(x))\). This draft suggests 'If I eat \(x\), then \(x\) must have a face.' This is not the intent of the original sentence.

Correct the Formula

The correct formula incorporating the context of the sentence (I don't eat anything that has a face) would be \(\forall x, F(x) \rightarrow \neg E(x)\). This formula correctly states that for every \(x\), if \(x\) has a face, then I do not eat \(x\).