Logic and Proof Exercises

Example 1

"All cats are cute" into p → q form.

Hint

Translating it into If-Then form might be a good stepping stone.

Example 2

"iPods are mp3 players" into p → q form.

Hint

The conclusion typically comes at the end of the statement.

Example 3

What is the converse of the statement "I cry whenever I watch P.S. I Love You"?

Hint

The converse is switching the hypothesis and the conclusion. And let's see you watch P.S. I Love You without tearing up.

Example 4

What is the inverse of the statement, "If it is a high school, then it is a learning institution"?

Hint

Inverses negate everything. No, they don't. Yes, they do.

Example 5

What is the contrapositive of the statement "All statements have contrapositives"?

Hint

Don't let the statement itself confuse you.

Example 6

"Peanut butter and jelly sandwiches contain jelly." Is the converse of the statement true or false? Is the inverse of the statement true or false? Is the contrapositive true or false?

Hint

The contrapositive is the inverse of the converse. Makes sense, right?

Logic and Proof Exercises

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

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