Q:

Question: Write the converse, inverse, and contrapositive of the following statement: "If I study for my math test, then I will get a good grade."

Accepted Solution

A:
A conditional statement consists of two parts, a hypothesis p in the β€œif” clause and a conclusion q in the β€œthen” clause, or mathematically you can write [tex] p\rightarrow q [/tex].In your example "If I study for my math test, then I will get a good grade" the hypothesis is p="I study for my math test" and the conclusion q="I will get a good grade".To form the converse of the conditional statement, interchange the hypothesis and the conclusion ([tex] q\rightarrow p [/tex]). In your case the converse statement is "If I will get a good mark, then I study for my math test."To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion ([tex] \neg p\rightarrow \neg q [/tex]). In your case the inverse statement is "If I do not study for my math test, then I will not get a good mark."To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement ([tex] \neg q\rightarrow \neg p [/tex]). In your example the contrapositive statement is "If I will not get a good mark, then I do not study for my math test."