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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