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Reasoning and Logic

Day 3: Symbolic Logic & Compound Statements

Slide 2

Today's Objectives

Slide 3

Warm-Up: True or False?

  1. Roanoke is in Virginia.
  2. A square has 5 sides.
  3. 2 + 3 = 5.
Slide 4

Compound Statements

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

Today's operators are:

~

NOT

∧

AND

∨

OR

Slide 5

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)

Slide 6

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)

Slide 7

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)

Slide 8

Guided Practice

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

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

  1. What is the truth value of p ∧ q?
  2. What is the truth value of p ∨ q?
  3. What is the truth value of ~p ∨ q?
Slide 9

Independent Practice

Choose your level and solve the problems.

RED (Developing)

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 (Applying)

Given p: "5 is an odd number" (True) and q: "4 is an odd number" (False).

  1. What is the truth value of p ∧ q?
  2. What is the truth value of p ∨ q?
  3. What is the truth value of ~p ∨ q?

GREEN (Securing)

Let p represent "x > 10" and q represent "x is even."

  1. Translate "x > 10 and x is even" into symbols.
  2. If x = 12, what is the truth value of p ∧ q?
  3. If x = 7, what is the truth value of ~p ∨ q?
Slide 10

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?