Truth Trees

Question 1

what is decomposing

Answer 1

breaking down statements into substatements

Question 2

what is possible if the truth value of a statement is known

Answer 2

the statement can be broken down into to sub-statements and their truth values can also be known

Question 3

what is the difference between single and double branching statements

Answer 3

single branching statements lead from one true statement directly to the next true statement

double branching statements lead in two possible outcomes

Question 4

what are the three single branching statements and their decompositions

Answer 4

x&y x y

~(xvy) ~x ~y

~(x→y) x ~y

Question 5

what are the two double branching statements with two decomposed sub-statements

Answer 5

x<->y x y or ~x ~y

~(x<->y) x ~y or ~x y

Question 6

what are the 3 double branching to single sub-statements statements

Answer 6

~(x&y) ~x ~y

xvy x y

x→y ~x y

Question 7

steps for solving problems with truth trees

Answer 7

1. set the problem to be solved as the trunk of the tree
2. use the rules for the 8 basic SL statements to draw the branches
3. if at least one branch is left open then one interpretation makes the statement true

if no branches are left open no single interpretation makes the statement true