Construct a truth table for ~q p
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Construct a truth table for ~q^p and submit it to the drop box
To construct a truth table for the logical expression ~q p, you need to consider all possible combinations of truth values for the variables q and p. Here's how you can do it step by step:
1. Identify the distinct variables in the expression: q and p.
2. Determine the number of rows in the truth table by calculating 2^n, where n is the number of distinct variables. In this case, since there are two variables (q and p), you will have 2^2 = 4 rows.
3. Create the column headers for q, p, ~q, and ~q p.
4. List down all possible combinations of truth values for q and p. In this case, there are four combinations:
a. q = true, p = true
b. q = true, p = false
c. q = false, p = true
d. q = false, p = false
5. Fill in the values for q and p in the respective columns.
| q | p | ~q | ~q p |
|-------|-------|-------|-------|
| true | true | | |
| true | false | | |
| false | true | | |
| false | false | | |
6. Calculate the negation (~) of q for each combination. Negation (~) inverts the truth value. So, if q = true, ~q = false; if q = false, ~q = true. Fill in the values for ~q.
| q | p | ~q | ~q p |
|-------|-------|-------|-------|
| true | true | false | |
| true | false | false | |
| false | true | true | |
| false | false | true | |
7. Finally, calculate the logical conjunction (AND) of ~q and p for each combination. Conjunction (AND) is true only when both operands are true. Fill in the values for ~q p.
| q | p | ~q | ~q p |
|-------|-------|-------|-------|
| true | true | false | false |
| true | false | false | false |
| false | true | true | true |
| false | false | true | false |
And there you have it – the complete truth table for the logical expression ~q p.