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Q5.

Expert-verified
Found in: Page 211

### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

# 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 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.