Finite Mathematics : Logic, Sets, and Counting

Study concepts, example questions & explanations for Finite Mathematics

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Example Questions

Example Question #41 : Logic, Sets, And Counting

Consider the logical proposition:

"William Shakespeare is dead."

True or false: The proposition "William Shakespeare is alive" is the negation of that statement.

Possible Answers:

True

False

Correct answer:

True

Explanation:

The negation of a proposition is the proposition "Not ," or, "It is not true that ."

The negation of "William Shakespeare is dead" is "It is not true that William Shakespeare is dead," or, simply, "William Shakespeare is alive."

Example Question #42 : Logic, Sets, And Counting

In order to win the grand prize in a lottery, the six numbers that come up must match the six numbers you chose; the order in which they come up need not be the same as the order on your ticket.

Is this is an example of a permutation or a combination?

Possible Answers:

Permutation

Combination

Correct answer:

Combination

Explanation:

A combination is defined as an unordered subset of a set; a permutation is an ordered subset. The key to answering this question is the phrase " the order...need not be the same." This is an indication that this is a combination.

Example Question #42 : Logic, Sets, And Counting

Try without a calculator:

Which of the following is equal to ?

Possible Answers:

Correct answer:

Explanation:

For any whole numbers , where ,

Setting :

.

Example Question #43 : Logic, Sets, And Counting

Consider the conditional statement

"If , then every duck is a bird."

Give the truth value of this statement.

Possible Answers:

True

The statement has no truth value.

False

Correct answer:

True

Explanation:

This conditional statement has a false antecedent , so, by the principles of logic, it is considered to have truth value "true." The truth value of the consequent is irrelevant.

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