SYMBOLISM Conditional Implication Ifthen clause symbol If antecedent

SYMBOLISM

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. A.

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

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

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

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

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:

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

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 propoor. E • L

Other words that can be symbolized by the • are: a) but f) however b) yet g) moreover c) also h) nevertheless d) still i) though e) although j) even though

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.

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.

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

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

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

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

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).

2. The negation of a disjunction may be expressed by using the neithernor 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 )

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)

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

EXERCISE: 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.

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.

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.

. 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) 1

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)

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)