2.5 Equivalent Statements

Create a truth table to determine whether the following compound statements are logically equivalent.

1. $p \rightarrow q ;$ $\sim p \rightarrow \text{ } \sim q$
2. $p \rightarrow q ;$ $\sim p \lor q$

Use the statements, $p$: Harry is a wizard and $q$: Hermione is a witch, to write the following statements:

1. Write the conditional statement, $p \rightarrow q$, in words.
2. Write the converse statement, $q \rightarrow p$, in words.
3. Write the inverse statement, $\sim p \rightarrow \text{ } \sim q$, in words.
4. Write the contrapositive statement, $\sim q \rightarrow \text{ } \sim p$, in words.

Use the conditional statement, “If all dogs bark, then Lassie likes to bark,” to identify the following.

1. Write the hypothesis of the conditional statement and label it with a $p$.
2. Write the conclusion of the conditional statement and label it with a $q$.
3. Identify the following statement as the converse, inverse, or contrapositive: “If Lassie likes to bark, then all dogs bark.”
4. Identify the following…

Assume the conditional statement, $p \rightarrow q :$ “If Chadwick Boseman was an actor, then Chadwick Boseman did not star in the movie Black Panther” is false, and use it to answer the following questions.

1. Write the converse of the statement in words and determine its truth value.
2. Write the inverse of the statement in words and determine its truth value.
3. Write the contrapositive of the statement in words and det…