Podcast
Questions and Answers
What distinguishes a predicate from a proposition?
What distinguishes a predicate from a proposition?
- A predicate has a fixed truth value.
- A predicate can only be represented by lowercase letters.
- A predicate depends on one or more variables. (correct)
- A predicate is always True.
If the statement ‘x is a power of 2’ is considered a predicate, what must be true about the variable x?
If the statement ‘x is a power of 2’ is considered a predicate, what must be true about the variable x?
- x can only be a positive number.
- x must be a constant value.
- x can take on any value from a domain. (correct)
- x must always be an integer.
Which of the following represents a correct example of a predicate?
Which of the following represents a correct example of a predicate?
- S: 10 is greater than 20
- R: x is a prime number (correct)
- P: x > 5 (correct)
- Q: 2 + 2 = 4
Why is the statement ‘7 is a power of 2’ classified as a proposition rather than a predicate?
Why is the statement ‘7 is a power of 2’ classified as a proposition rather than a predicate?
What is the codomain of a predicate?
What is the codomain of a predicate?
When does a predicate become a proposition?
When does a predicate become a proposition?
Which letter is typically used to represent predicates in mathematical logic?
Which letter is typically used to represent predicates in mathematical logic?
What will the statement ‘x is an even number’ evaluate to if x is replaced with 3?
What will the statement ‘x is an even number’ evaluate to if x is replaced with 3?
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Study Notes
Predicates
- Predicates are statements whose truth value depends on one or more variables from a set.
- A predicate is a function whose codomain is the set {True, False}, and whose domain can be any set.
- An example of a predicate is "x is a power of 2," where the variable x can take on any value.
- To determine the truth value of a predicate, we must substitute values for the variables.
- Predicates can depend on more than one variable. For example, "x^2 = y" is a predicate with two variables, x and y.
- We typically use uppercase letters starting from P to represent predicates.
- When values are substituted for the variables in a predicate, the resulting statement becomes a proposition.
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