Quiz 5 1.5, 3.1 Methods of Proof.

Quiz 5: Th. May pm 1) Give 2 rules of inference and the tautologies on which they are based. 2) Explain what an indirect proof is and explain why it is a valid strategy to prove an implication of the form p  q. 3) What is a vacuous proof? (explain). 4) Determine whether the following arguments are valid: a) “If x^2 is irrational then x is irrational”, ” the number x=1/3 is not irrational”, “therefore: the number x^2=(1/3)^2 is not irrational”. b) “Joe’s coat fits in his bag” “Joe’s bag fits in his car” “Therefore: Joe fits in his car”.

Answers Quiz 5 1) Give 2 rules of inference and the tautologies on which they are based. - see book 2) Explain what an indirect proof is and explain why it is a valid strategy to prove an implication of the form p  q. - you prove the equivalent propsoition: (NOT q)  (NOT p) 3) What is a vacuous proof? (explain). - You prove p  q by showing that p is always false, i.e. F  q is always true. 4) Determine whether the following arguments are valid: a) “If x^2 is irrational then x is irrational”, ” the number x=1/3 is not irrational”, “therefore: the number x^2=(1/3)^2 is not irrational”. - yes valid: p  q AND (NOT q)  (NOT p). b) “Joe’s coat fits in his bag” “Joe’s bag fits in his car” “Therefore: Joe fits in his car”. -No not valid: one could conclude that Joe’s coat fits in his car, but not Joe itself.