# Conjunctions and disjunctions

### Conjunctions and disjunctions

#### Lessons

Notes:

A conjunction is a compound statement that is made by combining two or more statements with the word "and". If any of the statements is false, then the entire conjunction is false. If all statements are true, then the conjunction is true. We can replace the word "and" with the symbol ˄.

A disjunction is a compound statement that is made by combining two or more statements with the word "or". If any of the statements is true, then the entire disjunction is true. If all statements are false, then the disjunction is false. We can replace the word "or" with the symbol ˅.

• Introduction
Conjunctions and Disjunctions Overview:
a)
Conjunctions

b)
Disjunctions

• 1.
Conjunctions

Determine the truth value of the following conjunctions:

a)
A square is a 4-sided polygon and a rectangle is a 5-sided polygon

b)
$10+7\times 2=72$ and $10\times 7+2=72$

c)
March is the third month of the year and December is the last month of the year

• 2.
The symbols represent the following statements:

$p$: A year has 52 weeks
$q$: December is a summer month
$r$: A kilogram is 1000 grams

Find the truth value of the following:
a)
$p$ ˄ $q$

b)
$p$ ˄ $r$

c)
$p$ ˄ ~$q$

d)
~$r$ ˄ ~$p$

e)
$p$ ˄ ~$q$ ˄ $r$

f)
~$p$ ˄ $q$ ˄ ~$r$

• 3.
Disjunctions

Determine the truth value of the following disjunctions:

a)
1 metre is 100 centimetres or 1 metre is 10 centimetres.

b)
A right triangle always has an angle that is 90° degrees or the angles of a square are always 90° degrees.

c)
Breakfast is a meal or all meals are breakfasts.

• 4.
The symbols represent the following statements:

$p$: A week has 5 days
$q$: A day has 24 hours
$r$: An hour has 60 seconds

Find the truth value of the following:
a)
$p$ ˅ $q$

b)
$p$ ˅ $r$

c)
$p$ ˅ ~$q$

d)
~$r$ ˅ ~$p$

e)
~$p$ ˅ $q$ ˅ ~$r$

f)
$p$ ˅ ~$q$ ˅ ~$r$

• 5.
Advanced Questions on Conjunctions and Disjunctions

Let $p$ and $q$ be statement. Fill in the blanks:

a)
If $p$ is false, then $p$ ˄ $q$ is _______________.

b)
If $p$ is true, then $p$ ˅ $q$ is _______________.

c)
If ~$p$ is true, then $p$ ˄ $q$ is _______________.