Formation Trees

Question 1

An argument like (¬A ∨ B) → (C & ¬(A ∨ D)) is not easy to what?

Answer 1

Keep track of what each intermediate column should be

Question 2

What is a way of breaking down the problem into smaller pieces?

Answer 2

A formation tree

Question 3

When we form sentences with logical operators, such as A => B, the logical operator is what?

Answer 3

The main connective

Question 4

What is the main connective in this sentence?
A & (B ∨ C)

Answer 4

&

Question 5

What is the main connective in this sentence?
(¬T ∨ P) → (G & ¬(P ∨ Q))

Answer 5

→

Question 6

How do we split up the sentence (A → B) & ¬A)?

Answer 6

Starting at the main connective, and then breaking down each branch (if it is not a single letter) at its main connective:
(A → B) & ¬A
/ \
(A → B) ¬A
/\ |
A B A

Question 7

From this formation tree, what are the two intermediate columns we need to establish?
(A → B) & ¬A
/ \
(A → B) ¬A
/\ |
A B A

Answer 7

(A → B) and ¬A

Question 8

Where does one start determining truth values from the formation tree?

Answer 8

The bottom, with the atomic sentences, and then work upwards

Question 9

What would the truth table for the following be?
(A → B) & ¬A
/ \
(A → B) ¬A
/\ |
A B A

Answer 9

A B |A → B |¬ A| (A → B) & ¬ A
T T T F F
T F F F F
F T T T T
F F T T T