2. WHAT IS LOGIC?
It allows us to determine the validity of arguments in and
out of Mathematics
It is a science or discipline that deals with the correct way
of reasoning.
ARISTOTLE – the father of Logic, the first person who
organized the study of logic.
Logic comes from the Greek word “logos” which means
speech and reasoning.
3. A proposition is a declarative statement that is, by itself,
either true or false “but not both”
Ex. The sun rise in the east every night.
TYPES OF PROPOSITION
a. Simple – means single idea statement.
b. Compound – conveys two or more ideas can be created
using logical connectives
PROPOSITION
CONJUNCTION
DISJUNCTION
CONDITIONAL
BICONDITIONAL
NEGATION
4. To every proposition is assigned a truth value. A true
proposition has a truth value “true” and a False proposition has a
truth value “false”. Sometimes, the symbols T or 1 are used for true
propositions and F or 0 are assigned to false propositions.
Typically, to denote a proposition, we shall use lower case
letters such as p, q, or r. These are called propositional variables or
sentential variables.
When a sequence of letter and/or logical connectives are given
such that when the variables are replaced by specific sentences, a
proposition is formed, then we call these sequence of symbols as
sentential form of the proposition.
PROPOSITION
5. To define a proposition, say p, we usually write:
p: <given statement>
For instance,
p: the earth has two moons.
q: seven divides 21.
t: Melissa drives a pink D-max.
PROPOSITION
7. Consider the following sentences. Determine if the
sentences are declarative or not and identify the truth
value.
______________ 1. 2 is the only even prime number.
______________ 2. 8 is a multiple of 10.
______________ 3. Mothers are proud of their children.
______________ 4. Are you happy?
______________ 5. x + 3 = 0
______________ 6. Clean the room before you go.
______________ 7. It will rain today.
______________ 8. Happy birthday!
LETS
TRY!!!
Declarative - True
Declarative - False
Declarative
Not a proposition -
Not Declarative – Interrogative
Declarative
Not a proposition -
Not Declarative – Imperative
Declarative
Not a proposition -
Not Declarative – Exclamatory
8. Identify whether the following statements are propositions. If it
is a proposition, determine its truth value.
1. p: 3 + 9 = 12
2. q: 3x – 2 = 13 when x is 5.
3. r: Dogs fly.
4. s: There are 31 days in the month of September.
5. t: 𝟏𝟐 is a rational number.
LETS
TRY!!!
---- Proposition <True>
---- Proposition <True>
---- Proposition <False>
---- Proposition <False >
---- Proposition <False>
9. Identify whether the following statements are propositions. If it
is a proposition, determine its truth value.
6. a: x + 9 = 11
7. b: y is less than 5
8. c: Please open the door.
9. d: x(0) = 0
10. e: c(0) = 1
LETS
TRY!!!
---- Not a Proposition
---- Not a Proposition
---- Not a Proposition
---- Proposition <True>
---- Proposition <False>
Depends on the value of x
16. Charlotte needs to go to work and Paulo is sick.
Charlotte needs to go to work but Paulo is sick.
Gladys is getting married and Tim is excited.
Either the dog is adorable or is playful.
The dog is either adorable or is playful.
Nikki wants to go to Paris or to London.
Nikki wants to go either to Paris or to London.
17. Joan is counting her calories and Jovel doesn’t
want to eat dessert.
The dog is not adorable and it is playful.
The dog is not adorable but it is playful.
Charlotte doesn’t needs to go to work or Paulo
is not sick.
Nikki doesn’t want to go to Paris and she wants
to go to London.
22. If it is raining then the sun is not shining.
If it is raining then the ground is wet.
The ground is wet if and only if it is raining
and the sun is not shining.
29. 1. 10 is not an even integer if and only if 11 is not a
prime number.
2. If 11 is prime number then 10 is not an even
integer.
3. It is not true that 11 is prime number while 10 is
not an even integer.
4. 10 is an even integer if and only if 11 is not a
prime.
~p ↔ ~q
q → ~p
~q ^ ~p
p ↔ ~q
