Law Of Syllogism

Which law of logic is this?

If I clean the bathroom, then I don't have to do the dishes.

I cleaned the bathroom.

Therefore, I don't have to do the dishes.

• Law of Detachment

• Law of Syllogism

• Law of Contrapositive

• None

Draw a conclusion from the statement.
If you go fishing, then you will need to bring your fishing rod.
You go fishing.

• You will need to bring your fishing rod.
• Invalid
• You are a boring person.
• You are going to catch a fish.

Draw a conclusion from the statement.
If a whole number is even, then its square is divisible by 4.
The number I am thinking of is an even number.

• Then it's not odd.
• Then it's a whole number.
• Then its square is divisible by 4
• Then it's even.

p→q
q→r
∴p→r
Which law is modeled?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

Draw a conclusion from the statement.
If Jack goes to school, then it is Monday.
Jack doesn't go to school.

• Jack skipped school.
• It isn't Monday.
• It's Saturday.
• Invalid

Use Law of Syllogism to make a conclusion.
 If a number is divisible by 10, then it is divisible by 2.  If a number is divisible by 2, then it is even.

• If a number is divisible by 10, then it is even,
• If a number is even, then it is divisible by 10.
• If a number is divisible by 2, then it is even.
• If a number is even, then it is divisible by 2.

p→q
p
∴q
Which law is modeled?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

Draw a conclusion from the statement.
If you live in Orlando, then you live in Florida.
You live in Orlando.

• You live in Disney Land
• You are an old person.
• You live in Florida
• You live in Orlando

If you go to the swimming pool, then you will enjoy yourself. If you enjoy yourself, you will want to return.

• If you return to the pool you will enjoy yourself.

• If you enjoy yourself, then you went to the pool.

• If you go to the pool, you will want to return.

• No conclusion can be made.

Write the if-then statement that follows from the pair of true statements. If Todd goes to the movies, then Sarah will go to the movies.  If Chris goes to the movies, then Todd will go to the movies.

• If Chris goes to the movies, then Sarah will go to the movies.
• If Todd goes to the movies, then Chris will go to the movies.
• If Sarah goes to the movies, then Chris will go to the movies.
• If Chris goes to the movies, then Todd will go to the movies.