Given the conditional statement "If it is Friday, then my friends and I order pizza." find the following in symbols and in words. a: It is Friday. b: My friends and I order pizza. The converse in symbolic form is O \( a \rightarrow \sim b \) \( \sim b \rightarrow \sim a \) \( \sim a \rightarrow \sim b \) O \( a \rightarrow a \) The converse in word form is If my friends and I do not order pizza, then it is not Friday. If my friends and I order pizza, then it is Friday. If it is not Friday, then my friends and I do not order pizza. If it is Friday, then my friends and I order pizza.

Let's break down the given conditional statement and identify the components step by step. ### Given Conditional Statement: "If it is Friday, then my friends and I order pizza." ### Step 1: Identify the Components - **a**: It is Friday. - **b**: My friends and I order pizza. ### Step 2: Symbolic Representation - **a**: \( a \) - **b**: \( b \) The original conditional statement can be represented symbolically as: \[ a \rightarrow b \] ### Step 3: Converse of the Statement The converse of a conditional statement \( p \rightarrow q \) is \( q \rightarrow p \). Therefore, the converse of our statement \( a \rightarrow b \) is: \[ b \rightarrow a \] ### Step 4: Evaluate the Given Options for the Converse The options provided are: 1. \( a \rightarrow \sim b \) 2. \( \sim b \rightarrow \sim a \) 3. \( \sim a \rightarrow \sim b \) 4. \( a \rightarrow a \) None of these options correctly represent the converse \( b \rightarrow a \). ### Step 5: Word Form of the Converse The word form of the converse \( b \rightarrow a \) is: "If my friends and I order pizza, then it is Friday." ### Summary - **In Symbols**: - a: \( a \) - b: \( b \) - Original Statement: \( a \rightarrow b \) - Converse: \( b \rightarrow a \) - **In Words**: - a: It is Friday. - b: My friends and I order pizza. - Original Statement: If it is Friday, then my friends and I order pizza. - Converse: If my friends and I order pizza, then it is Friday.