Answer to Question #326302 in Discrete Mathematics for Ama trump

Question

a)​Establish that: is a tautology.

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​b)​Translate in two ways each of these statements into logical expressions ​using predicates, quantifiers, and logical connectives. First, let the ​domain consists of the students in your class and second, let it consist ​of all people.

​i) Everyone in your class has a mobile phone.

​ii) Somebody in your class has seen a foreign movie.

​iii) There is a person in your class who cannot swim.

​iv) All students in your class can solve quadratic equations.

​v) Some students in your class does not want to be rich.

​c)​Prove that if m + n and n + p are even integers, where m, n, and

​p are integers, then m + p is even. What kind of proof did you use?

​d)​Prove, by induction that: 2 divides whenever n is a positive

​integer.