CSE 260- 001
QUIZ-5– Proofs - ANSWER
(30 points/ 20 minutes)
NAME:
1. (6 points) Show that p→qis proved by showing q true.
Hint: if q is true you have to consider the following two cases:
p q
--------
T T
F T
p=T and q=T gives p→q=T
p=F and q=I gives p→q=T
2. (6 points) Let P,Qand Rbe three compund propositions. Consider the following
general description of an inference rule:
P
Q
Therefore, R
Above inference rule makes the statement P∧Q→Ra tautology because when P,
Qare true Ris true (from the inference rule) and the statement is true; for the other
cases one of Por Qwill be false and the statement is also true.
Consider the inference rule Modus ponens:
p
p→q
therefore, q
Show by truth table p∧(p→q)→qis a tautology.
p q p →q p ∧(p→q)p∧(p→q)→q
T T T T T
T F F F T
F T T F T
F F T F T
You are given the following statements:
3. a) All clear explanations are satisfactory.
b) Some excuses are unsatisfactory.
c) Some excuses are not clear explanations.
Prove formally that (c) follows from (a) and (b).
