WEEK 2

LESSON LEARNING OUTCOME:

At the end of this lesson, students are able to:

Define predicate logic.
State the expression of predicate in statement.
Identify the compound statement in predicate logic.
Compare the type of quantifier in: Universal; Existential.
Identify the quantified statements.
Write a well-formed predicate logic in English sentence.
Transfer the translation with quantifiers.

DEFINE PREDICATE

"A predicate is a verb-phrase template that describes a property of objects, or a relationship among objects represented by the variables. "

The propositional logic is not powerful enough to represents all types of assertions that are used in computer science and mathematics, or to express certain types of relationship between propositions such as equivalence. Hence, to cope with the deficiencies of propositional logic, we introduce two new features: PREDICATE and QUANTIFIERS.

EXAMPLE 1:

The sentences:

"The car, Mr. Karim is driving is blue."

"The sky is blue."

"The cover of the book is blue."

See any similarities in the sentences above??

EXAMPLE 2:

EXAMPLE 3:

More than 1 variable can involve with a predicate.

QUICK EXERCISE 1

Let G(x,y) represent the predicate x>y.

a. G(6,13) means 13 is greater than 6.

b. G(2,0)

c. G(7,1) means 7 is greater than 1.

d. "4 is less than 5" can be represented by G(5,4).

Let E(x,y) represent "x sent an email to y".

a. ~E(Maria, Nick) means Maria did not send an email to Nick.

b. E(A,B) = E(B,A)

c. "B send an email to A" is represented by E(B,A).

(True / False)

QUANTIFIER

UNIVERSAL QUANTIFIER

EXISTENTIAL QUANTIFIER

HOW TO READ QUANTIFIED FORMULAS

Let a domain of discourse be a set of cars and let predicate F(x,y) denote "x is faster than y". Hence:

∀x∀y F(x,y): “Every car is faster than every car”.
∀x∃y F(x,y): “Every car is faster than some cars”.
∃x∀y F(x,y): “Some cars are faster than every car”.
∃x∃y F(x,y): “Some cars are faster than some cars”.

QUICK EXERCISE 2

Write this predicate logic in English sentences and vice versa.

Let E(x) = "x is an even number" and G(x,y) = "x > y". Let the domain of discourse be the set of natural numbers.

∀x∃y G(x,y)
∃x∀y G(x,y)
∃x ~E(x)
~∀x E(x)
6 is an even number
Some numbers are greater than some numbers.
Some numbers are greater than 10.

QUICK EXERCISE 3

Construct a true statement by using "all" or "some" based on the object and properties given

a. Object: Vehicles

Property: Four wheels

b. Object: Rectangle

Property: Four angles

Construct a false statement by using "all" or "some" based on the object and properties given:

a. Object: Bus

Property: Four wheels

b. Object: Triangle

Property: Three angles

WEEK 2 ACTIVITY

Kindly complete the activity for Week 2 lesson as follows:

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