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Q5.

Expert-verified

Geometry

Found in: Page 211

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

For each statement in Ex 5-10 copy and complete a table like the one shown below.

Statement	If ?, then ?	True/false
1. Given	if I live in Los Angeles, then I live in California.	True
2. Contrapositive	if I do not live in California, then I do not live in Los Angeles.	True
3. Converse	if I live in California, then I live in Los Angeles.	False
4. Inverse	if I do not live in Los Angeles, then I do not live in California.	False

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Define contrapositive, inverse, and converse for the given statement

If the given statement is ‘’If p then q’’, the contrapositive is ‘’If not q then not p’’.

If the given statement is ‘’If p then q’’, the converse is ‘’If q then p’’.

If the given statement is ‘’If p then q’’, the inverse is ‘’If not p then not q’’.

Step 2. Contrapositive of the given statement

The given statement is if I live in Los Angeles, then I live in California and this is true.

Since Los Angeles lies in the basin in southern California.

Therefore, the given statement is if I live in Los Angeles, then I live in California and this is true.

The contrapositive of the given statement is if I do not live in California, then I do not live in Los Angeles.

Thus, it is also true.

Step 3. Check inverse and converse of the given statement

The converse of the given statement is if I live in California, then I live in Los Angeles.

Thus, it is false.

The inverse of the given statement is if I do not live in Los Angeles, then I do not live in California.

Thus, it is false.

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