LESSON #29
Rules of Replacement II
Reading Assignment: 7.4 (pp. 395-400)
Click here to bypass the following discussion and go straight to the assignment.
Transposition:
| This rule writes out the thought behind MT in one line. Given that P É Q, if Q is false then P will be false too. | (p É q) º ( ~q É ~p) |
Material Implication:
| This is another very useful rule. It is the only rule which allows you to change between a É and a v. Notice that the antecedent of the É statement gets negated when changing between É and v. Given P É Q , there are two possible states of affairs. P could be false. If that is so, we don't know about Q. Or P could be true, in which case Q is true as well. | (p É q) º ( ~p v q) |
Material Equivalence:
| This is the only rule which involves a º . Any time you want to work with a º you will use one of these rules. These are three different ways of saying the same thing--either p and q are both true or they are both false. | [(p º
q)] º [ ( p É
q) · (q É
p)]
[(p º q)] º [ (p · q) v (~p · ~q)] |
Exportation:
| Exportation is a very specific rule. You will use it rarely. But don't forget that it is there if you get stuck. | [(p · q) É r ]º[ p É (q É r)] |
Tautology:
| Simply reminds you that p v p and p · p actually are equivalent to p. |
p º (p v p) p º (p · p) |
Logic Coach Assignment: 7.4 I all, II 1-16, III 1-4.
Assignment ( 20 points each)
Using all the rules of inference, derive the conclusions of the following symbolized arguments.
NOTE: Be sure to copy down the problems neatly and correctly!
A) 1. (C É D) É (G É K)
B) 1. J º Q
2. J É
(Q É O)
3.
~O
// ~Q
C) 1. F É (A ·
K)
2. G É
(~A · ~K)
3. F v
G
// A º K
D) 1. ( X É Y) ·
(~P É ~Q)
2. (H É
Q) · (~H É
~Y) // X É
P
E) If congress enacts a law that either establishes a religion or prohibits the free exercise of religion, then that law is unconstitutional. Therefore if congress enacts a law that establishes a religion, then that law is unconstitutional.