# Kenneth Rosen Edition 7th Exercise 1.4 Question 26 (Page No. 54)

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Translate each of these statements into logical expression in three different ways by varying the domain and by using predicates with one and with two variables.

1. Someone in your school has visited Uzbekistan.
2. Everyone in your class has studied calculus and C++.
3. No one in your school owns both a bicycle and a motorcycle.
4. There is a person in your school who is not happy.
5. Everyone in your school was born in the twentieth century.

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Suppose the domain of the propositional function $P(x,y)$ consists of pairs $x$ and $y$ , where $x$ is 1,2 or 3 and $y$ is 1,2 or 3 . Write out these propositions using disjunctions and conjunctions. $\exists x P(x,3)$ $\forall y P(1,y)$ $\exists y \sim p(2,y)$ $\forall x \sim P(x,2)$