Construct a truth table for ~q ->(p V q)
Whew! Lot of truth tables. I think you need some practice. You try this one.
lol i know right!! i hate the truth tables too!! i think this is it:
T T F
F T T
F F F
T T F
There are a few typos in your chart...
TTF
TFF
FFT
FTT ??
Interesting, only the fourth row is correct.
Here is the correct one.
p......q......~q......p V q......~q --> (p V q)
T......T.......F..........T...................T
T......F.......T..........T...................T
F......T.......F..........T...................T
F......F.......T..........F...................F
Okay....thanks :)
To construct a truth table for the statement ~q -> (p V q), we need to consider all possible combinations of truth values for the variables q and p. Here's how to do it step by step:
Step 1: Identify the variables
In the given statement, the variables are q and p.
Step 2: Create the column headers
Create column headers for q, p, ~q, p V q, and ~q -> (p V q).
Step 3: Determine the number of rows
The number of rows needed can be determined by calculating 2 raised to the power of the number of variables. Since there are two variables (q and p), we will have 2^2 = 4 rows.
Step 4: List all possible combinations
List all possible combinations of truth values for the variables q and p. In this case, there are four possible combinations:
- q = true, p = true
- q = true, p = false
- q = false, p = true
- q = false, p = false
Step 5: Calculate the values for ~q and p V q
Calculate the truth values for ~q and p V q based on the defined combinations.
Here's a completed truth table:
| q | p | ~q | p V q | ~q -> (p V q) |
|-----|-----|-----|-------|--------------|
| T | T | F | T | T |
| T | F | F | T | T |
| F | T | T | T | T |
| F | F | T | F | F |
In the truth table, T represents true and F represents false. Hence, the truth table for the statement ~q -> (p V q) is complete.