SOLUTION: please help me slove this question . Construct a truth table for each compound statement. 1-q ∨ (p ∧ ∼q) 2- ∼q ∧ (∼ p ∨

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Question 232782: please help me slove this question .

Construct a truth table for each compound statement.

1-q ∨ (p ∧ ∼q)


2- ∼q ∧ (∼ p ∨ ∼q)
Answer by vleith(2983)   (Show Source): You can put this solution on YOUR website!
Let's do the first one, then you cna use the same technique to do the second one
Create a table that has 5 rows (one for the headings, one each for the combination of 0 and 1 for the variables p and q)
Then add an column for each 'term' in the given logical statement. In this case, you need p, q, ~q, (p^~q) and finally p v (p^~q). So you need 5 columns, as shown below.
Then add in the true/false (1/0) entries for p and q. Since there are two variables with two possible values, you have 2*2 total. Or 4 rows of info.

p q ~q (p^~q) pv(p^~q)
0 0
1 0
1 0
1 1

Now complete the ~q column, given the entered values for p and q
p q ~q (p^~q) pv(p^~q)
0 0 1
1 0 1
0 1 0
1 1 0
Now complete the (p^~q) column, given the entered values for p and ~q
p q ~q (p^~q) pv(p^~q)
0 0 1 1
1 0 1 1
0 1 0 0
1 1 0 1
Finally complete the pv(p^~q) column, given the entered values for p and (p^~q)
p q ~q (p^~q) pv(p^~q)
0 0 1 0 0
1 0 1 1 1
0 1 0 0 0
1 1 0 0 1

Here's a nice URL for truth tables http://www.brian-borowski.com/Software/Truth/

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