How can I draw the truth table for the following? :
((non p) ,(non q)) and non (p or q)
and, what can you conclude from these tables?
Ok make the chart for it but I will help you if you can give the exact problem and use ~ for non p
For ex.
~p
~q
p ~p
T F
F T
q ~q
T F
F T
p q (p∨q) ~(p∨q)
T T T F
T F T F
F T T F
F F F T
Note: ~(p∨q) = ~p ∧ ~q
Ok, fine ill try with this.
P Q ~P ~Q P v Q ~P v ~Q
T T F F T F
T F F T F F
F T T F F F
F F T T F T
When doing column three, look at column 1.
When doing column four, look at column 2.
When doing column 5, look at column 1 and 2
When doing column 6, look at column 3 and 4.
And follow the rules of conjunction and disjunction.
priscilla, stop it.
To draw a truth table for the given expression, ((¬p) ,(¬q)) ∧ ¬(p ∨ q), follow these steps:
1. Identify the variables: In this case, the variables are p and q.
2. Determine the number of rows: Since there are two variables (p and q), the truth table will have 2^2 = 4 rows.
3. Set up the headings: Create columns for p, q, ¬p, ¬q, (¬p,¬q), p ∨ q, and ¬(p ∨ q).
4. Fill in the values: Start with the leftmost columns for p and q. Switch the values in each row, so each column alternates between true (T) and false (F). For example, the first few rows would be: T, T, F, F.
5. Calculate the rest of the values: Fill in the columns for ¬p (negation of p), ¬q (negation of q), (¬p,¬q) (the conjunction of ¬p and ¬q), p ∨ q (the disjunction of p and q), and finally, ¬(p ∨ q) (the negation of (p ∨ q)).
6. Complete the truth table: Fill in the final values for each row.
Once you have the completed truth table, you can analyze the output to draw conclusions. Look for patterns or relationships between the inputs (p and q) and the output of the expression ((¬p) ,(¬q)) ∧ ¬(p ∨ q).
For example, you can determine whether the expression is always true (T) or always false (F) based on the values in the final column. You can also look for specific combinations of inputs that result in a true or false output.
Remember, this specific expression is ((¬p) ,(¬q)) ∧ ¬(p ∨ q). Analyzing the truth table for this expression will provide insights into the conditions under which it evaluates to true or false.