Truth Values and Predicates

The video tutorial explains logical statements, which are either true or false, and introduces predicates, which are mathematical phrases dependent on variables. It discusses how predicates become logical statements when specific values are assigned to variables. An example is given with the predicate P of X, where X is a factor of 12, and the concept of truth set and false set is introduced. The truth set is demonstrated with factors of 12.

What is a logical statement?

• A statement that is either true or false.

• A statement that is neither true nor false.

• A statement that is always false.

• A statement that is always true.

Which of the following is an example of a logical statement?

• X is less than 10.

• X is a factor of 12.

• V is greater than 2.

• X is greater than 5.

Why is 'X being greater than 5' not a logical statement?

• Because it contains a variable.

• Because it is always false.

• Because it is always true.

• Because it is a mathematical sentence.

What makes a mathematical sentence not a statement?

• It is a complex equation.

• It is always true.

• It contains a variable.

• It is always false.

What is a predicate in mathematical terms?

• A mathematical phrase dependent on variables.

• A complex equation.

• A statement that is always true.

• A logical statement.

How does a predicate become a logical statement?

• By changing the domain.

• By plugging in specific values for the variables.

• By adding more variables.

• By removing the variables.

What is the domain of the predicate P(X) in the example?

• All integers.

• Negative integers.

• Positive integers.

• All real numbers.

What is the truth value of P(6) if P(X) is 'X is a factor of 12'?

• Depends on the context

• Neither true nor false

• True

• False

Why does P(1/3) not make sense in the given predicate example?

• Because 1/3 is a factor of 12.

• Because 1/3 is not a positive integer.

• Because 1/3 is a negative integer.

• Because 1/3 is a real number.

What is a truth set?

• A set of all integers.

• A set of all possible values.

• A set of values that make a predicate false.

• A set of values that make a predicate true.