******** * remember: * no CS 100 lecture this FRIDAY, October 12 * that's why HOMEWORK 6's paper is due 11:00 am on MONDAY, October 15 ******** * ONE MORE EXAMPLE: * If the Green Party loses in the local election, then the developer-friendly politicians will have a majority in the city council. * If the developer-friendly politicians have a majority in the city council, then the city council will vote down restrictions on development on agricultural land. * It is NOT the case that the city council will vote down restrictions on development on agricultural land OR that the Green Party will lose in the local election. * THEREFORE, it is NOT the case that IF the Green Party does NOT lose in the local election, THEN the city council will NOT vote down restrictions on development of agricultural land. * IDENTIFY the simple statements in the argument, and give each a letter P = the Green Party loses in the local election Q = the developer-friendly politicians will have a majority in the city council R = the city council will vote down restrictions on development on agricultural land * now rewrite the argument in prop logic form: P -> Q Q -> R ~(R v P) ∴ ~( ~P -> ~R ) * make a TRUTH TABLE for this argument, and MARK the columns that represent the premise(s) and conclusion: (*) (*) (*) (C) P Q R P->Q Q->R RvP ~(RvP) ~P ~R ~P->~R ~(~P->~R) ------------------------------------------------------------ T T T T T T F F F T F T T F T F T F F T T F T F T F T T F F F T F T F F F T T F F T T F F T T T T T F T F F T F T F T F F T T T T F F F T T T T F T F F T F F F T T F T T T T F ...and, as shown on document camera, when we cross out all the rows where any premise is F, there is only 1 row left where all 3 premises are true, and in THAT the Conclusion is false, SO: this argument is NOT valid (all of its premises being true does NOT guarantee that its conclusion is true) * NEXT: a little programming! with WeScheme (www.wescheme.org)