If q is true and r is false, what is the truth value of ~r∧~(q∨r)?truefalsecannot be determinedSubmit

The given statement is ~r∧~(q∨r).

Let's break it down:

1. ~r: The negation of r. Given that r is false, ~r is true.

2. q∨r: The disjunction of q and r. This is true if either q or r is true. Given that q is true and r is false, q∨r is true.

3. ~(q∨r): The negation of q∨r. Given that q∨r is true, ~(q∨r) is false.

4. ~r∧~(q∨r): The conjunction of ~r and ~(q∨r). This is true if both ~r and ~(q∨r) are true. Given that ~r is true and ~(q∨r) is false, ~r∧~(q∨r) is false.

So, the truth value of ~r∧~(q∨r) is false.