Q:Question:a. The mortgage rate went down, if and only if Lionel purchased the house and the down payment was \( 10 \% \). b. The down payment was \( 10 \% \), and if Lionel purchased the house then the mortgage rate went down. c. If Lionel purchased the house, then the mortgage rate went down and the down payment was not \( 10 \% \). Q.7 Determine whether the following argument is valid or invalid. (Why?) If Chicago is north of the United States,