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Unformatted text preview: Let’s build a truth table for the fairly com plicated sentence ( A → (( M ∨ G ) → ∼ B )) & ∼ G The first step is to identify the claim vari ables in the target sentence. They are { A,B,G,M } . Next, we start off our blank table with reference columns and the target sentence. A B G M ( A → (( M ∨ G ) → ∼ B )) & ∼ G Next, we determine how many rows our table will require. Since our target sen tence ( A → (( M ∨ G ) → ∼ B )) & ∼ G has 4 claim variables, the table will have 2 4 (or 16 ) rows. Now, we fill out the reference columns for our 16 row table. Let’s start from the rightmost reference column. A B G M ( A → (( M ∨ G ) → ∼ B )) & ∼ G T F A B G M ( A → (( M ∨ G ) → ∼ B )) & ∼ G T F T F T F T F T F T F T F T F A B G M ( A → (( M ∨ G ) → ∼ B )) & ∼ G T T T F F T F F T F T F T F T F T F T F A B G M ( A → (( M ∨ G ) → ∼ B )) & ∼ G T T T F F T F F T T T F F T F F T T T F F T F F T T T F F T F F A B G M ( A → (( M ∨ G ) → ∼ B )) & ∼ G T T T T T F T F T T F F F T T F T F F F T F F F T T T F F T F F T T T F F T F F A B G M ( A → (( M ∨ G ) → ∼ B )) & ∼ G T T T T T F T F T T F F F T T F T F F F T F F F T T T T T F T F T T F F F T T F T F F F T F F F A B G M ( A → (( M ∨ G ) → ∼ B )) & ∼ G T T T T T T T F T T F T T T F F T F T T T F T F T F F T T F F F F T T T F T T F F T F T F T F F F F T T F F T F F F F T F F F F Now, we have to start filling out the columns un der the sentence ( A → (( M ∨ G ) → ∼ B )) & ∼ G We’ve got to pick the smallest subsentences and first work out what goes under them, and so on. The smallest subsentences are { M ∨ G, ∼ B, ∼ G } . It doesn’t matter what order we go in. Let’s work right to left. To help make it completely clear what is going on, I will flag the column we are filling out with a ‘ ⇓ ’ symbol, and the columns whose values the ‘working’ column is a function of with a ‘ ↓ ’ symbol. Finally, going through this example truthvalue by truthvalue would be painful — there are 96 values to fill out. Thus, I will do them in small clusters....
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This note was uploaded on 03/19/2010 for the course PHIL Phil210 taught by Professor Sasdas during the Spring '10 term at Concordia Canada.
 Spring '10
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