Part 1. Which of the following arguments are valid? Explain your reasoning. (a) I have a student in my class who is getting an A. Therefore, John, a student in my class, is getting an A. (b) Every Girl Scout who sells at least 30 boxes of cookies will get a prize. Suzy, a Girl Scout, got a prize. Therefore, Suzy sold at least 30 boxes of cookies. Part 2. Determine whether cach argument is valid. If the argument is valid, give a proof using the laws of logic. If the argument is invalid, give values for the pred- icates P and Q over the domain a, b that demonstrate the argument is invalid. (a) Ir (P(z) ^ Q(z)) arQ(z) ^ Ir P(z) | (b) VI (P(z) V Q(x)) (z)d #A ^ (1)dFA"

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Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.