Construct a truth table for q ->~p
q p ~p q->~p
T. T. F. F
T. F. T. T
F. T. T. T
F. F. T. T
i definitely don't understand truth tables....thanks for your help :)
To construct the truth table for the expression q -> ~p, we need to consider all possible combinations of truth values for the variables q and p.
Step 1: Identify the variables involved in the expression.
In this expression, we have two variables: q and p.
Step 2: Determine the number of rows in the truth table.
Since we have two variables, there are 2^2 = 4 possible combinations of truth values.
Step 3: Assign truth values to the variables in the truth table.
We assign the truth values true (T) and false (F) to q and p.
q | p | ~p | q -> ~p
____________________________
T | T | F | F
T | F | T | T
F | T | F | T
F | F | T | T
Step 4: Evaluate the expression.
To evaluate q -> ~p, we need to apply the logical implication operator (->) and negation (~) to the truth values of q and ~p.
For each row, we look at the combination of q and ~p, and determine the truth value of q -> ~p using the following rule:
- If q is false (F), then q -> ~p is true (T) regardless of the truth value of ~p.
- If q is true (T), then q -> ~p is true (T) only if ~p is true (T), otherwise it is false (F).
In our case, for each row in the truth table, we apply this rule to fill in the truth values for the expression q -> ~p.
q | p | ~p | q -> ~p
____________________________
T | T | F | F
T | F | T | T
F | T | F | T
F | F | T | T
So, the truth table for the expression q -> ~p is as shown above.