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: 40

Answer

The truth value of the conditional statement is true. Consider the provided statement, “If the country is Spain, then the age of marriage with parental consent is\[18\]”. In the above statement, take the country, Spain as \[p\]and the age of marriage with parental consent,\[18\] 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, Spain and the \[q\]statement is also true, which is the age of marriage with parental consent is\[18\]. So, from the above, the conditional statement will be also true and it can write in the form of a table:
1566403188

Work Step by Step

The converse of the statement is: If the age of marriage with parental consent is18, then the country is Spain. The inverse of the statement is: If the country is not Spain, then the age of marriage with parental consent is not18. The contrapositive of the statement is: If the age of marriage with parental consent is not18, then the country is not Spain. Further, the converse and the inverse are not necessarily true, but the contrapositive of the statement is true.
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