Formal Logic Drills

Unless I am sleeping, I am watching animal planet.

-Sleeping --> Animal Planet

There are no unicorns without vivid rainbows.

-Vivid rainbows --> -Unicorns

Acorns fall from trees, if and only if, the bells ring.

Acorns fall --> Bells ring Bells ring --> Acorns fall These are not contrapositives, they are two different statements.

If it's an apple, then it is neither a vegetable, nor an android.

Apple ---> -Vegetable AND -Android

If it's an apple, then it is a fruit OR the daughter of Gwen.

Apple ---> Fruit OR Daughter of Gwen

All apples are fruits.

Apple --> Fruit

An apple is always a fruit.

Apple --> Fruit

An apple is required to be a fruit.

Apple --> Fruit

Any apple is a fruit.

Apple --> Fruit

Being an apple depends on being a fruit.

Apple --> Fruit

Every apple is a fruit.

Apple --> Fruit

If it's an apple, then it's a fruit.

Apple --> Fruit

It's a fruit, if it is an apple.

Apple --> Fruit

It's an apple, only if it is a fruit.

Apple --> Fruit

To be an apple, it must be a fruit.

Apple --> Fruit

When it's an apple, it's a fruit.

Apple --> Fruit

If it's an apple, then it is a fruit, but not a vegetable.

Apple --> Fruit AND -Vegetable.

Numbers Deductions: A --> B -B --> -A

B, Neither, or Both Never A

Numbers Deductions -A --> B -B --> A

Both, A, B Never neither

With "if and only if" and "if but only if" phrases we can have...

Both, or neither terms.

The only time I eat cake, is on my birthday.

Cake --> Birthday

Red velvet and chocolate cake, are the only types of cake that I eat

Cakes I eat --> Red velvet OR Chocolate NOTE: We use OR instead of AND because we are not eating both cakes at the same time, just specifying which types we like.

Diving legally requires a license.

Diving legally --> License

Only lemons are fruits.

Fruit --> Lemon

If it is a grape, then it is not an acorn.

Grape --> -Acorn

Frogs are green, if gumdrops are green.

Gumdrops green --> Frogs green

If I have ice cream, then I will also have candy or cookies, but not both.

Ice cream --> Candy OR Cookies NOTE: The two above statements are written as if "but not both" is omitted from the sentence. Without "but not both" we could technically have all three (candy and cookies) However, the "but not both" tells us that if we have candy and cookies we cannot have ice cream.

It is not a mammal or it does not lay eggs, unless it is a platypus.

Mammal AND Legs --> Platypus

Numbers Deductions A --> -B B --> -A

Neither, A, B Never both

You cannot pass the course unless you pass final, or write a paper.

Pass class --> Pass final OR Write paper

Peaches are blue, if but only if, zoos are blue.

Peaches blue --> Zoos blue OR Zoos blue --> Peaches blue These are not contrapositives, they are two different statements.

I'll go to the movie, unless Nicholas Cage is in it.

Translate via "if not." Change "unless" into "if not." -NC --> Go to movie.

Anne is on vacation, unless Steve is on vacation.

Translate via "if not." Change "unless" into "if not." -Steve ---> Anne

Without struggle, there is no progress.

Translate via "if not." Change "without" into "if not." -Struggle --> -Progress

It's not an apple, unless it is a fruit.

Translate via arrow approach. Cross out "not" and make if. Then draw arrow through unless and you get: Apple --> Fruit

An apple is never a vegetable.

Two step process to translation: 1. Draw arrow. 2. Place your "no" on right hand side of arrow. 3. After step two, it does not matter how you order terms. Correct answers: Apple --> -Vegetable Vegetable --> -Apple

No apple is a vegetable.

Two step process to translation: 1. Draw arrow. 2. Place your "no" on right hand side of arrow. 3. After step two, it does not matter how you order terms. Correct answers: Apple --> -Vegetable Vegetable --> -Apple

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