consider the conditional statement...
\if you go to office hours, then you pass the test.\
a) write the converse of the original statement:
if select an answer, then select an answer.
b) write the inverse of the original statement:
if select an answer, then select an answer.
c) write the contrapositive of the original statement:
if select an answer, then select an answer.

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Converse Inverse Contrapositive" ], "new_concepts": [], "current_concepts": [ "Conditional Statements", "Converse Inverse Contrapositive" ] } ## Identify components of the conditional statement $$ \begin{aligned} &p: \text{"you go to office hours"} \ &q: \text{"you pass the test"} \ &\text{Original statement } (p ightarrow q): \text{"If you go to office hours, then you pass the test."} \end{aligned} $$ ## Formulate converse, inverse, and contrapositive $$ \begin{aligned} &\text{Converse } (q ightarrow p): \text{"If you pass the test, then you go to office hours."} \ &\text{Inverse } ( eg p ightarrow eg q): \text{"If you do not go to office hours, then you do not pass the test."} \ &\text{Contrapositive } ( eg q ightarrow eg p): \text{"If you do not pass the test, then you do not go to office hours."} \end{aligned} $$ Consider the conditional statement... "If you go to office hours, then you pass the test." a) Write the converse of the original statement: If you pass the test, then you go to office hours. b) Write the inverse of the original statement: If you do not go to office hours, then you do not pass the test. c) Write the contrapositive of the original statement: If you do not pass the test, then you do not go to office hours. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Converse Inverse Contrapositive" ] }

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Question

Explanation:

Identify components of the conditional statement

Formulate converse, inverse, and contrapositive

Answer: