Write an equivalent statement that does not use the if ... then connec $\text { Use the fact that } p \rightarrow q \text { is equivalent to } \sim p \vee q \text {. }$
-If your shoes need polishing, you take them to Jack's place.
A)Your shoes do not need polishing or you take them to Jack's place.
B)Your shoes do not need polishing or you do not take them to Jack's place.
C)Your shoes need polishing so you take them to Jack's place.
D)Your shoes need polishing and you do not take them to Jack's place.

Question

Quizplus · Accepted Answer

The original statement "If your shoes need polishing, you take them to Jack's place" can be represented as $p \rightarrow q$, where $p$ is "your shoes need polishing" and $q$ is "you take them to Jack's place". According to the equivalence $p \rightarrow q \equiv \sim p \vee q$, the equivalent statement is "Your shoes do not need polishing or you take them to Jack's place", which matches choice A.

Write an Equivalent Statement That Does Not Use the If Use the fact that p→q is equivalent to ∼p∨q. \text { Use the fact that } p \rightarrow q \text { is equivalent to } \sim p \vee q \text {. } Use the fact that p→q is equivalent to ∼p∨q.

Write an Equivalent Statement That Does Not Use the If $\text { Use the fact that } p \rightarrow q \text { is equivalent to } \sim p \vee q \text {. }$