A particular system specifies that a valid password must include at least three different types of characters $($uppercase characters, lowercase characters, digits, and non$-$alphanumeric characters$).$ You would like to create a propositional logic statement that expresses this idea.

You recognize that this requirement includes the following propositions:

$s=$ the password contains uppercase letters $t=$ the password contains lowercase letters $u=$ the password contains digits $v=$ the password contains non$-$alphanumeric characters

a$.$ Write a logic expression that is true when at least three of $\{s,t,u,v\}$ are true.

b$.$ How many rows will be in a truth table for this expression?

c$.$ Write the complete truth table for this expression.

$($Hint: The final column of your truth table will be true in exactly five cases.$)$