- Sections 1.1-1.3,21-2.2. Vocabulary - Set, element, subset. Cartesian product, relation. - Statement form, variable, corverse, inverse, negation, contrapositive. - Truth table, logically equivalent. Problem'1 1. Create set A to be all the people in your group, set B to be all the people in your group who are taking COMP 1001 this term, and set C to be all the people in your group who are taking a non-science course this term. How are A, B, and C related? How many elements are in each set? 2. Find the Cartesian product of A and B. How many elements are in this set? 3. Define a relation R from A to Bas follows: - Given any (x,y)AB,(x,y)R means that x is taking a class with y this term (do not count COMP 1002). - State explicity which ordered pairs are in R. - What are the domain and co-domain of R?Z. - Is R a subset of A? Is R a subset of AB ? 4. Create an Arrow Diagram for R from part 3. Problem, 2 1. Consider the statement form ((pq)p)p. Construct a truth table and determine whether it is a tautology. contradiction, or nelther, 2. Write the Comerss. Imerse Negation. Contrapositive of the statement form in part 1. For each, determine whether it is a tautology, contradiction, or neither. Problem 3 1. Use the laws of Theorem 2.11 to verify the following equivalence. Supply a reason for each step. - pa (qp)=p 2. Use the laws of Theorem 2.1.1. to verify the following equivalence. Supply a reason for each step. pvq)(pa)=p Problem 4. Exta Imagine you are at a restarrant and at the table next to you is a child with their guardian. Consider the following? - Eating broccoll com and protein are necessary for the chlld to finish their dinger. - The guardias tels the child "if you finish your dinner, then you cas eat dessere' - The child does not eat broccoll. 1. Define the progositional variables you will use in your elaboration Using these varlables, write the sentences in itallossin statement form and fil in a truth table. 2 Determine if it is possibie for the child to not eat broccoli and still eat dessert. Discuss. 3. Write the Comverse Inverse Nceation Contrepositive of the guardian's statement. Are any of these logically equivalent to each other or to the guardian' paternent? 4. What happers if we roplaced the guardaris statement with the Convilss, heverse, Contrapositioc Does the chad always get dessert whenever they: at their broccoll