Predicate Logic, and Predicate Form.

Question

I am currently researching mathematics, and I am currently stumped on Predicate Logic. I was just wondering how to put this statement into predicate form. "Each Student must play at least 2 sports" thank you in advance.

Answer 1

One defines a set $S$ of different kinds of sports and a set $T$ of students. A relation $R \subseteq T \times S$ is defined to be true if a student $t$ plays the sport $s$, i.e. $(t,s) \in R$.

Now your statement means $$ \forall t \in T, \exists s_1, s_2 \in S \text{ such that } (t,s_1) \in R, (t,s_2) \in R \text{ and } s_1 \ne s_2. $$