Texts: questions 2, 3, and 4. Please explain answers.
Complete a well-organized write-up with clear answers or proofs to the following. Demonstrate appropriate work and justification of solutions. [Note: Your write-up will be evaluated on its mathematical correctness and completeness AND the quality and clarity of its presentation. Note: For assignment problems, collaboration with other people and use of online resources is NOT permitted.]
Questions for Assignment #3
1. For each of the following, use rules of inference to show that the given hypotheses imply the given conclusion. Show the argument in a formal step-by-step, Step-Reason table. Note: Be sure to clearly declare whatever propositional variables or propositional functions you introduce to interpret these statements in logical symbolism.
a) The hypotheses "If Jerry eats ramen or the delivery app is working, then Jerry buys soy sauce.", "Jerry eats ramen or Jerry eats hot dogs.", and "Jerry is from New York City." imply "Jerry buys soy sauce."
b) "Every person who plays the violin has taken music lessons." and "Beth has not taken music lessons." imply "Beth does not play the violin." [Note: Assume the implied domain is the domain of all persons and that Beth is a member of this domain.]
2. Using direct proof, prove that for a real number x, if x is rational, then 4 + 3 is rational.
3. Using proof by contradiction, prove that if x is an irrational number, then 5x + 3 is an irrational number.
4. Prove, using fundamental definitions, that the following statements about an integer n are equivalent: i) n is odd, ii) n + 4n is odd.
