Podcast
Questions and Answers
What distinguishes a predicate from a proposition?
What distinguishes a predicate from a proposition?
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?
Which of the following represents a correct example of a predicate?
Which of the following represents a correct example of a predicate?
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?
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What is the codomain of a predicate?
What is the codomain of a predicate?
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When does a predicate become a proposition?
When does a predicate become a proposition?
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Which letter is typically used to represent predicates in mathematical logic?
Which letter is typically used to represent predicates in mathematical logic?
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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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Description
This quiz covers the concept of predicates, their definitions, and examples in logical statements. It discusses how predicates determine truth values based on variable substitution and introduces related terminology. Test your understanding of predicates and their applications in logic.
