2/9 2. Logical Connectives and Symbolic Translation Online Quiz Questions

Let $p$ mean “The museum is open” and $q$ mean “I have a reservation.” Which symbolic statement means “The museum is open and I have a reservation”?

The disjunction $p \lor q$ is true when both $p$ and $q$ are true.

In the conditional $p \to q$, what is the logical name for the first proposition, $p$?

For which truth-value assignment is the conditional $p \to q$ false?

Select all statements that correctly describe the biconditional $p \leftrightarrow q$.

In standard propositional logic, a conditional $p \to q$ is true whenever its antecedent $p$ is false.

What English connective phrase is represented by $p \leftrightarrow q$?

Select all expressions that are logically equivalent to $p \to q$ according to the material.

Let $p$ mean “The security code is valid,” $q$ mean “the account is active,” and $r$ mean “access is granted.” Which expression translates “If the security code is valid and the account is active, then access is granted”?

Explain the truth conditions for the conditional $p \to q$. Identify exactly when it is false and explain why the cases with a false antecedent are considered true.

Using the stated order of operations for logical connectives, which part is evaluated first in the expression $\lnot p \lor q \to r$?

Let $p$ mean “Maya submitted the form” and $q$ mean “Maya paid the fee.” Which symbolic expression represents “Maya submitted the form and paid the fee”?

In standard propositional logic, the disjunction $p \lor q$ is true when both $p$ and $q$ are true.

Let $p$ mean “You may enter” and $q$ mean “You have a ticket.” Which symbolic expression translates “You may enter only if you have a ticket”?

Enter the logical symbol for the biconditional connective, which represents “if and only if.”

Suppose $p$ is false and $q$ is false. What is the truth value of $p \leftrightarrow q$, and why?

Let $p$ mean “the application is complete,” $q$ mean “the fee is paid,” and $r$ mean “the request will be processed.” Enter the symbolic translation of “If the application is complete and the fee is paid, then the request will be processed.”

For the conditional $p \to q$, which assignment of truth values makes the statement false?