Aim: Logic – Conjunction/Disjunction Course: Math Lit.

Do Now:

Aim: What is the conjunction and disjunction of the truth?

True or False

Math is a 4-letter word and 4th period starts at 10:25 am.

George Washington was the first president of the United States and John Lennon is alive.

T

F

Aim: Logic – Conjunction/Disjunction Course: Math Lit.

Compound Statement

A compound statement is formed by combining simple statements with one or more operators.

“and” is and operator and is represented symbolically as ˄

Conjunction

Math is a 4-letter word and 4th period starts at 10:25 am.

T

George Washington was the first president of the United States and John Lennon is alive.

F

Aim: Logic – Conjunction/Disjunction Course: Math Lit.

Conjunction - Symbolically

Let p represent the simple statement

“The earth is a spherical ball.”

Let q represent the simple statement

“The earth is the third planet in our solar system.”

T

T

The earth is a spherical ball and the earth is the third planet in our solar

system.

p ˄ q

T

Aim: Logic – Conjunction/Disjunction Course: Math Lit.

Symbolic

Let p represent the simple statement

“Kobe Bryant is a basketball player.”

Let q represent the simple statement

“Derek Jeter is a basketball player.”

T

F

Kobe Bryant is a basketball player and Derek Jeter is a basketball player.

p ˄ q

F

Aim: Logic – Conjunction/Disjunction Course: Math Lit.

Evaluating the Truth

Let p represent the simple statement

“The Mets are a baseball team based in Los Angeles.”

Let q represent the simple statement

“The Jets are a football team based in Chicago.”

F

F

The Mets are a baseball team based in Los Angeles and The Jets are a football

team based in Chicago.

p ˄ q

F

Aim: Logic – Conjunction/Disjunction Course: Math Lit.

Truth Table - Conjunction

p q p ˄ q

T T T

T F F

F T F

F F F

If p and q represent simple statements then the truth table for compound statements with the ‘and’ operator (Conjunction) is

Aim: Logic – Conjunction/Disjunction Course: Math Lit.

Evaluating the Truth

Let p represent “Staten Island is a borough of NYC.”

Let q represent “SI is connected to Brooklyn via the Verrazano Bridge.”

Let r represent “SI has a greater population than Brooklyn.”

T

T

F

What is the truth value of the following?

a) p ˄ r b) p ˄ ~r

c) ~p ˄ ~r d) p ˄ q ˄ ~r

Aim: Logic – Conjunction/Disjunction Course: Math Lit.

Model Problem

p q

T

T

F

F

T

F

T

F

T

F

F

T

T

F

F

F

T

F

T

T

Construct the truth table for the following:

~( ~p ˄ q )

~p ~p ˄ q ~(~p ˄ q)

Aim: Logic – Conjunction/Disjunction Course: Math Lit.

Disjunction

“or” is and operator and is represented symbolically as ˅

Disjunction

A compound statement is formed by combining simple statements with one or more operators.

Home plate is 60’ 6” from the pitching mound or a football field is 100 yards long.

First base is 90 feet from home plate or a football field is 100 feet long.

The Petrides school is located in Brooklyn or October follows November in the calender year.

T

T

F

Aim: Logic – Conjunction/Disjunction Course: Math Lit.

Truth Table - Disjunction

p q p ˅ q

T T T

T F T

F T T

F F F

If p and q represent simple statements then the truth table for compound statements with the ‘or’ operator (Disjunction) is

Aim: Logic – Conjunction/Disjunction Course: Math Lit.

Symbols Words

Let m represent “The grass is green.”

Let n represent “The hit was a single.”

Let s represent “The first baseman made the out.”

Rewrite:

a) m ˅ n

b) ~n ˅ s

c) ~n ˅ ~s

The grass is green or the hit was a single.

The hit was not a single or the first baseman made the out.

The hit was not a single or the first baseman did not make the out.

Aim: Logic – Conjunction/Disjunction Course: Math Lit.

Order of Operations

Parentheses indicate order of operations.

~(n ˄ m)? negation of the statement ‘n and m”

Ex. n is a true statement and c is a false statement. What is the truth value of the compound statement

(n ˅ c) ˄ ~(n ˄ c)

(T ˅ F) ˄ ~(T ˄ F)

T ˄ ~(F)

T ˄ T

T

Aim: Logic – Conjunction/Disjunction Course: Math Lit.

Model Problem

Construct a truth table for the following compound statement:

~(p ˄ q) ˄ [(p ˅ q) ˄ q]

p q

T

T

F

F

T

F

T

F

p ˄ q

T

F

F

F

F

T

T

T

T

T

T

F

T

F

T

F

F

F

T

F

~(p ˄ q) p ˅ q [(p˅q)˄q] ~(p˄q)˄[(p˅q)˄q]

Aim: Logic – Conjunction/Disjunction Course: Math Lit.

Model Problem

Suppose p is T and q if F. Find the truth values for the following statements.

Let p: I eat spinach. q: I am strong.

a) ~(p ˄ q)

b) ~p ˄ q