6.4_-_symbolism_ppt (1).ppt AAAAAAAAAAAA

Hello!

2. A.Conditional (Implication),
If-then clause ( symbol >, → )
If – antecedent
then - consequent
A conditional statement or an
implication is easily
recognizable because of the
if-then clause.

3. Example:
1. If Shalani will host the program,
then she will sing. H > S
2. If Lio will recite a poem, then
he will not dance. R > ~ D
3. If the price of oil will increase,
then the daily fare will
increase. P > F

4. Other words than can
substitute the if-then clause
are:
a) implies g) entails
b) in case h) only if
c) provided that
d) given that
e) necessary condition
f) sufficient condition

5. Note: There is no change in
the meaning of the
conditional statement (#3
above) even if we re-state
it as:
1. If the price of oil will
increase, the daily fare will
increase. P > F

6. 2. The increase in the price of oil
entails the increase in daily
fare. P > F
3. That there is an increase in
the daily fare is the necessary
condition for the oil price to
increase. P > F
4. The price of oil increases only
if the daily fare will increase.
P > F

7. The conditional statement
p > q (if p then q) means
that q is possible if p is said
to be realized. In like
manner, we can state it in
various ways without the
fear of misrepresentation
such as:

8. a) q if p
b) p implies q
c) p only if q
d) q in case p
e) q provided that p
  f) q given that p
g) q is a necessary condition
for p
h) p is a sufficient condition
for q

9. B. Conjunction, and (symbol •,
^)
Uses the word and to connect
two statements.
Example:
1. The president’s economic
agenda and the senate’s
legislative agenda are pro-
poor. E • L

10. Other words that can be
symbolized by the • are:
a) but f) however
b) yet g) moreover
c) alsoh) nevertheless
d) still i) though
e) althoughj) even though
 

11. C. Disjunction, or (symbol v)
Disjunction is a compound
statement expressing
alternate or disunion. To form
the disjunction, the English
phrase “either or" is used to
connect two simple
statements.

12. The word either is placed at
the beginning of the
statement while the word or
is inserted at the middle. The
meaning of the disjunction
does not change even if the
word “either” is not used.

13. Example:
1. Either the youth will hold a
party or they will go
swimming. P v S
The youth will hold a
party or they will go
swimming. P v S

14. 2. Either Carol will be a varsity
or she joins the choir.V v C
Carol will be a varsity unless
she joins the choir. V v C
Unless Carol joins the choir,
she will be a varsity. V v C

15. D. Negation, not (symbol ~ )
The negation of a statement
is simply done by inserting
the word “not” into the
statement.
Example:
1. The boy will not shoot the
ball. ~ S

16. Other words that can
substitute not in statements
are:
a) it is false that
b) it is not the case that
c) it is not true that

17. Remarks:
1. Punctuations are needed
to avoid ambiguity.
A v B • C is ambiguous.
It could mean
( A v B ) • C or
A v ( B • C).

18. 2. The negation of a disjunction
may be expressed by using the
neither-nor clause.
Example:
Either Harry or Ron will be
elected class president. H v R
Neither Harry nor Ron will be
elected president. ~ ( H v R )

19. 3. Care should also be
observed when using the
word “both” as follows:
The mayor and vice-mayor
alone will not both solve the
crime in their localities.
~ ( M • V )

20. The mayor and vice-mayor
alone will both not solve the
crime in their localities.
~ M • ~ V
Both the mayor and vice-
mayor alone will not solve the
crime in their localities. ~ M
• ~ V

21. 1. Either I attend my classes or
go to the mall.
2. Wakeboarding and bungee
jumping are the most
adventurous hobbies.
3. Buildings are strong enough
on condition that they
withstand earthquake.

22. 4. You will graduate with honors
only if you persevere.
5. Children will turn out spoiled
unless parents discipline them.
6. Either you to go the beach
or you stay home and be with
your family.

23. 7. Unless you take a rest, neither
can you eat your breakfast
nor go to school.
8. Either I will teach organic
chemistry or analytical
chemistry but if I teach both
then I might not teach discrete
mathematics.

24. 1. Rene and Blaise helped
David’s campaign yet John
is the winner. (R,B,J)
2. If either Cj or Alvin will go to
the party, then Sydney
will go swimming, and if Sydney
will not go swimming,
then Cj and Alvin will not both
go to the party. (C, A, S)

25. 3. Either you consult your
lawyer and file a complaint or
you’ll lose your job and be
penniless. (C,F,L,P)
4. If you prefer to have a party,
then you can invite all your
closest friends or just put the
money in the bank and use it
for business. (P,I,M,B)

26. 5. If you study your lesson
then you’ll pass the exam
or if you don’t study at all
then you’ll surely fail in the
exam. (F,P,S)