Textbook notes - Predicates and Quantifiers

Question 1

What two parts is the statement “x is greater than 3” made up of?

Answer 1

The variable “x” is the subject of the statement. The second part “is greater than 3” is the predicate.

Question 2

If we have the statement “x is greater than 3”, how can this be denoted as P(x)?

Answer 2

We can set P to denote the predicate “is greater than 3”, and x is the variable.

Question 3

When does the statement P(x) become propositional?

Answer 3

When a value is assigned to the variable X. There will be a truth value.

Question 4

The statement P(x) is also known as?

Answer 4

It is said to be the value of the PROPOSITIONAL FUNCTION P at x.

Question 5

Let J(x) denote the statement ‘student x is failing math’. Student Mary is failing math, but Sophie and James are not failing math. What are the truth values of J(Mary), J(Sophie) and J(James)?

Answer 5

J(Mary) is the only true statement here; the other two are false.

Question 6

Let E(x,y) denote “x=y-2”. What are the truth values of the propositions E(5,7) and E(2,10)?

Answer 6

E(5,7) is true, E(2,10) is false.

Question 7

What is a precondition?

Answer 7

A statement that describes valid input in computer programs.

Question 8

What is a postcondition?

Answer 8

The conditions a program should satisfy when the program has run.

Question 9

What are some words used in quantifications?

Answer 9

All, some, none, few