criticalthinkingttableeg20092010term2

criticalthinkingttableeg20092010term2 - Lets build a truth...

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Unformatted text preview: Lets 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. Lets 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 Weve 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 doesnt matter what order we go in. Lets 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 truth-value by truth-value would be painful there are 96 values to fill out. Thus, I will do them in small clusters....
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criticalthinkingttableeg20092010term2 - Lets build a truth...

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