1. An alert California teacher chided "Dear Abby" (Baltimore Sun, March 1, 1989) for her statement "Confidential to Eunice: All men do not cheat on their wives." Let p(x) be the statement "x cheats on his wife" in the universe of all men. Write Abby's statement symbolically. Rewrite the statement, using the existential quantifier. Do you think that the statement is true or false? What do you think Abby really meant to say?
2. Recently, as the Amtrak train pulled into the Baltimore station, the conductor announced, "All doors do not open." Since passengers were permitted to get off at the station, what do you think the conductor meant to say?