Reasoning and Logic

Day 3: Symbolic Logic & Compound Statements

Today's Objectives

Translate statements to and from symbolic form.
Understand and use the symbols for NOT, AND, and OR.
Determine the truth value of compound statements.

Warm-Up: True or False?

Roanoke is in Virginia.
A square has 5 sides.
2 + 3 = 5.

Compound Statements

A compound statement is formed by joining two or more statements with logical operators.

Today's operators are:

~

NOT

∧

AND

∨

OR

Negation (NOT)

The negation of a statement has the opposite truth value.

~p

Let p: "The sky is blue." (True)

~p: "The sky is not blue." (False)

Conjunction (AND)

A conjunction is only true when BOTH parts are true.

p ∧ q

Let p: "A triangle has 3 sides." (True)

Let q: "A square has 5 sides." (False)

p ∧ q: "A triangle has 3 sides and a square has 5 sides." (False)

Disjunction (OR)

A disjunction is true if AT LEAST ONE part is true.

p ∨ q

Let p: "A triangle has 3 sides." (True)

Let q: "A square has 5 sides." (False)

p ∨ q: "A triangle has 3 sides or a square has 5 sides." (True)

Guided Practice

Let p: "Rectangles have 4 right angles." (True)

Let q: "Triangles have 4 sides." (False)

What is the truth value of p ∧ q?
What is the truth value of p ∨ q?
What is the truth value of ~p ∨ q?

Independent Practice

Choose your level and solve the problems.

RED

Given p: "It is sunny" and q: "We go to the park."
1. Write the words for p ∧ q.
2. Write the words for p ∨ ~q.

YELLOW

Given p: "5 is odd" (T) and q: "4 is odd" (F).
1. Truth value of p ∧ q?
2. Truth value of p ∨ q?
3. Truth value of ~p ∨ q?

GREEN

Let p: "x > 10" and q: "x is even."
1. Translate: "x > 10 and x is even"
2. If x=12, truth value of p ∧ q?
3. If x=7, truth value of ~p ∨ q?

Exit Ticket

On your notecard:

Let p: "A square is a rectangle." (True)

Let q: "A rectangle is a square." (False)

1. Write the words for p ∧ q.

2. What is the truth value of p ∧ q?

3. What is the truth value of p ∨ q?

Geometry Presentation