Final answer:
To show that (a → b) ∧ (a ∧ ¬b) is a contradiction, we can use a truth table. The truth table demonstrates that the expression always evaluates to false, making it a contradiction.
Step-by-step explanation:
To show that (a → b) ∧ (a ∧ ¬b) is a contradiction, we can use a truth table. A truth table lists all possible combinations of truth values for the variables in the expression and evaluates the result for each combination.
In this case, we have two variables: a and b. We will list all possible combinations for a and b and evaluate the expression (a → b) ∧ (a ∧ ¬b) for each combination.
Here is the truth table:
ab(a → b)(a ∧ ¬b)(a → b) ∧ (a ∧ ¬b)truetruetruefalsefalsetruefalsefalsetruefalsefalsetruetruefalsefalsefalsefalsetruefalsefalse
As we can see from the truth table, the expression (a → b) ∧ (a ∧ ¬b) always evaluates to false. This means that it is a contradiction, as it is always false regardless of the values of a and b.