LOGIC LAWS

Law of Detachment

p q

p

_______

q

p q

~q

_______

~p

Modus Tollens

pq pq~p ~q

____ ____

q P

Law of disjunctive inference

Drawing Conclusions using the laws

• Given the three statements, what conclusion can be found?

• If Rachel joins baseball then Rachel likes to sing

• Rachel will join baseball or Rachel will play basketball

• Rachel does not like to sing

Rewrite the sentences into symbols:

BS

BA

~S

Try to find two statements that form a rule

BS

~S

You can use Modus tollens to conclude

~B

You then can use ~B to form a rule with BA

You can use the law of disjunctive inference to conclude A

Try:

Given:

If Billy misses the Yankees game then the red sox win

If the red sox win then Billy is not happy

Billy is happy

Prove:

Billy does not miss the Yankee game

Y: Billy misses the Yankee game

W: Red sox win

H: Billy is happy

Y: Billy misses the Yankee game

W: Red sox win

H: Billy is happy

Given:

YW

W ~H

H

Using Modus tollens

W ~H

H

Conclude

~W

Therefore using

Modus tollens

YW

~W

Concludes

~Y

So Billy does not miss the Yankee game

HOMEWORKPg. 79

4-18 even

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Pg. 84-85

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