Question

# Determine whether each statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. (1) If it is Tuesday, then Marla tutors chemistry. (2) If Marla tutors chemistry, then she arrives home at 4 P.M. (3) If Marla arrives home at 4 P.M., then it is Tuesday.

Solution

Verified
Step 1
1 of 2

Law of Detachment states if $p\Rightarrow q$ is true and $p$ is true, then $q$ is true. Law of Syllogism states if $p\Rightarrow q$ and $q\Rightarrow r$ are true, then $p\Rightarrow r$ is true.

Notice that Statement (3) is an If-then statement which means Law of Detachment can't be used since the conclusion of Law of Detachment is not an If-then statement.

For Statement (1), $p$ is it is Tuesday" and $q$ is Marla tutors chemistry". For Statement (2), $q$ is Marla tutors chemistry" and $r$ is she arrives home at 4 P.M." The conclusion using Law of Syllogism would then be the statement If it is Tuesday, then Marla arrives home at 4 P.M." Statement (3) is the converse of this conclusion so the statement is invalid.

## Recommended textbook solutions #### Geometry

1st EditionISBN: 9780076639298Carter, Cuevas, Cummins, Day, Malloy
4,577 solutions #### Geometry Common Core

1st EditionISBN: 9780133185829 (1 more)Basia Hall, Charles, Johnson, Kennedy, Dan, Laurie E. Bass, Murphy, Wiggins
5,531 solutions #### enVision Geometry

1st EditionISBN: 9780328931583 (4 more)Al Cuoco
2,702 solutions #### Big Ideas Math Geometry: A Common Core Curriculum

1st EditionISBN: 9781608408399 (2 more)Boswell, Larson
4,072 solutions