Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 3 - Logic - 3.5 Equivalent Statements and Variations of Conditional Statements - Exercise Set 3.5 - Page 171: 39

Answer

The truth value of the conditional statement is true.
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Work Step by Step

(a) Consider the provided statement, “If the country is Italy, then the age of sexual consent is\[14\]”. In the above statement take the country is Italy as \[p\]and the age of sexual consent is \[14\]as\[q\]. Then, the symbolic notation of the above statement is written below: \[p\to q\] Then from the graph, the \[p\]statement is true which is the country is Italy and the \[q\]statement is also true which is the age of sexual consent is\[14\]. So, from the above, the conditional statement will be also true and it can write in the form of a table: From, the table \[p\to q\] is a conditional statement and it is a true statement. Hence, the truth value of the conditional statement is true. (b) The converse of the statement is: If the age of sexual consent is14, then the country is Italy. The inverse of the statement is: If the country is not Italy, then the age of sexual consent is not14. The contrapositive of the statement is: If the age of sexual consent is not14, then the country is not Italy. Further, the converse and the inverse are not necessarily true. But, the contrapositive of the statement is true.
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