Propositional calculus (also called propositional logic, sentential calculus, sentential logic, or sometimes zeroth-order logic) is the branch of logic concerned with the study of propositions (whether they are true or false) that are formed by other propositions with the use of logical connectives, and how their value depends on the truth value of their components. Logical connectives are found in natural languages.

1. Do U argue logically?

2.  How?
 You say or propose a logical statement
 Your proposition is logical if the truth of the
statement can be determined.
 Your proposition is a statement if it states a logic.

3. Is it a statement?
Can it be determined whether it is true or
false?

4.  Carlos is a boy
 Is Carlos a boy?
 y$ + x$ = “boy”
 Pair up.
 Discuss the 3 expressions.
 Which one/s are logical propositions?

5.  Carlos is a boy
 Is Carlos a boy?
 y$ + x$ = “boy”
Truth can be checked.
Do not know y$ or x$,
therefore cannot determine
truth of the expression.
This is a question.
Not a statement.
Proposes - states

6.  So to be a proposition
 It should state something
 We should be able to determine the truth of the
statement
 Sometimes it is easier to determine the truth of a
negative statement:
 Carlos is not a tree

7.  The propositional statement can change,
therefore can it be called a variable? For
example:-
 Carlos is a girl or Carlos is a man or Carlos is a
woman, etc.
 Area of logic includes girl, man, woman, boy,
human, etc.
 Carlos is a boy  p

8.  p = Carlos is a boy
 Can the variable be T for True or F for False?
How?
 If Carlos is actually a man then
 Is p = T or p = F?
 If we want to state: Carlos is NOT a boy? How
can we write this?
 ¬

9.  p = Carlos is a boy
 If Carlos is actually a boy, is ¬ p true?
 Pair up. Decide on all possible combinations of
the variable p.
 Now put all combinations in a table.
 What can we call this table?

10.  Class to break up into four groups.
 Each group to take ONE problem and show the
solution on a poster.

11.  Which of these sentences are propositions? What
are the truth values of those that are
propositions?
 a) Boston is the capital of Massachusetts.
 b) Miami is the capital of Florida.
 c) 2 + 3 = 5.
 d) 5 + 7 = 10.
 e) x + 2 = 11.
 f ) Answer this question

12.  Which of these are propositions? What are the
truth values of those that are propositions?
 a) Do not pass go.
 b) What time is it?
 c) There are no black flies in Maine
 d) 4 + x = 5.
 e) The moon is made of green cheese.
 f ) 2n ≥ 100.

13.  What is the negation of each of these
propositions?
 a) Mei has an MP3 player.
 b) There is no pollution in New Jersey.
 c) 2 + 1 = 3.
 d) The summer in Maine is hot and sunny.

14.  What is the negation of each of these
propositions?
 a) Jennifer and Teja are friends.
 b) There are 13 items in a baker’s dozen.
 c) Abby sent more than 100 text messages
every day.
 d) 121 is a perfect square.