- #1

mathmari

Gold Member

MHB

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I am looking at the following:

translate the following statements into set inclusion.

(i) Those who drown are not a fish or a swimmer.

(ii) Scientists are human.

(iii) A person who is not a swimmer is a non-swimmer.

(iv) Fish are not human.

(v) There was a case of a drowned mathematician.

(vi) Mathematicians are scientists.

Check if from the statements (i)–(vi)

,,There was a mathematician who was not a swimmer”

can be implied.

I have done the following:

We consider the sets:

E =Set of drowning, F = Set of Fish, S = Set of swimmers, N = Scientists, H = Human, M = Mathematiker

We have then the following:

(i) $x\in E\rightarrow x\notin (F\cup S)$

(ii) $N\subseteq H$ i.e. $x\in N\rightarrow x\in H$

(iii) $x\in H : x\notin S \rightarrow x\in S^c$

(iv) $F\not\subseteq H$

(v) $\exists x \in (E\cap M)$

(vi) $M\subseteq N$

Is everything correct so far? Could I improve something?

The statement ,,There was a mathematician who was not a swimmer” could be formulated as followes, or not? $$\exists x\in M : x\in S^c$$