Scope: Propositions, Quantifiers, Proofs

Answer following 5 questions.

1.  Prove the logical equivalence of conditional statement and contrapositive of two propositional variables using truth table.

2. Which of the following five statements are propositions? If they are propositions, write the truth value of them. i) i)2 + 3 = 10

ii) Fire!!!

iii) p = 5

? iv) If ? ?n = 10, then 2?n ? = 1024.

v) Will you get A+ in discrete math?

3. Translate the following English sentences using predicates and quantifiers. Then, negate the following statements.

a."There is a good football player in the class", where domain consists of all students in the class.

b."All men must die", where domain consists of all male characters of the TV series "Game of Thrones".

4.Consider the following program segment.

x = 10; if (x > 5) y = 10;

if(y == 10) z = 20;

Which rule of inference is used here?

5.Prove by contrapositive. "If n?2? is odd, then n is odd."