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Chapter 3: Problem 36

Express each statement in "if ... then" form. (More than one correct wording in "if... then" form may be possible.) Then write the statement's converse, inverse, and contrapositive. Being a citizen is a necessary condition for voting.

Short Answer

Expert verified
The 'if-then' form is 'If you are voting, then you are a citizen'. The converse is 'If you are a citizen, then you are voting'. The inverse is 'If you are not voting, then you are not a citizen'. The contrapositive is 'If you are not a citizen, then you are not voting'.

Step by step solution

01

Conversion into if-then form

The 'necessary condition' denotes something that must be true for the consequent to occur. Therefore, the statement 'Being a citizen is a necessary condition for voting' translates into 'If you are voting, then you are a citizen'.
02

Writing the converse

The converse of a statement flips the if-then order. Thus, the converse to this statement would be 'If you are a citizen, then you are voting'.
03

Writing the inverse

The inverse of a statement flips the truth values of both the condition and the consequent. Thus, the inverse for this statement is 'If you are not voting, then you are not a citizen'.
04

Writing the contrapositive

The contrapositive of a conditional statement flips both the condition and the consequent, and also exchanges their truth values. Hence, the contrapositive to this statement will be 'If you are not a citizen, then you are not voting'.

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