Implication, or a conditional

Notice the phrase 'If it's raining, then the road became wet'. That phrase is a compound sentence, because it is formed by two statements, namely 'Now the rain' and 'roads become wet'. Note that the second sentence is linked by connective sentence 'If - Then -'. Any sentence of the form 'If p then q' is called a conditional (or implications), p is called the conditional hypothesis, q is called the conclusion of a conditional. Conditional 'if p then q', (consider if the same as if), symbolized by a p q (p implies q) . In everyday life, then the conditional word is often not mentioned. For example, if it's raining, the road became wet. Another way to write conditional is q if p (roads became wet when it's raining).

EXAMPLE

Using a symbolic representation

p: I'm healthy

q: I eat fast food.

r: I exercise regularly.

Express sentence under the representation simbolils.

a. I'm healthy when exercising regularly.

b. If I only eat fast food and do not exercise regularly, I was not feeling well.

COMPLETION

a. I'm healthy when exercising regularly is the conditional sentence "if - then - 'and can be represented again become

'if you exercise regularly, I am healthy'

then, this compound sentence is represented symbolically by r

b. If I only eat fast food and not exercising regularly, I was not feeling well. This sentence is conditional 'if - then -', but involving konsungsi and two negation in it. The symbolic representations of the above sentence is (q ^ ~ p) r.

EXAMPLE

Express sentence 'All men must die'

COMPLETION

sentence 'All human must die' can be denoted again if he is human, would die. Then, we define two symbolic sentence:

p: Something is a human

q: Human must die

sentence can be expressed p -> q. In general, the phrase 'all p then q' can be expressed p -> q

We have discussed how the compound statements are formed, the next we can give the truth value analysis.

compound statement	Symbols	Readings
Negation	~	notes
Conjunctions	^	and
disjunction	v	or
conditional / implications		if - then -

Disjunction, union and the sample space

Disjunction is formed when a few sentences connected by the word 'or'. Symbols used by the disjunction to represent the word 'or' is v. Thus, the disjunction of using 'pvq' to represent the sentence 'p or q'. We can interpret the word 'or' in two ways. Consider the following sentence:

p: Ahmad is a cadre PDIP
q: Syu'aib a cadre PDIP

Sentence Ahmad is a cadre of PDIP or Syu'aib is a cadre of PDIP may symbolized by p v q. Note that a possibility they can be a cadre PDIP together. In this example, we discuss about 'or' inclusive. Now consider the example

p: Ahmad is a cadre PDIP
q: Ahmad is a cadre of Democrats

In fact in our political world, it is very likely one man has two membership cadre. However, we assume each man only wanted to be a cadre in one party only. Thus, the two events are not likely to occur together. Technically, if the second sentence is true, then the combination of both false disjunction. In short one sentence mengexclude another sentence. Is called the disjunction Exclusive disjunction.

Conjunction, an intersection state

Consider the statement 'Abbas is a member of PMI and he Golkar Party cadres'. It is a compound sentence, since this sentence comes from two simple sentences - 'Abbas, a member of the Red Cross' and sentence 'He (Abbas) is the Golkar Party cadres' - and the conjunctive 'and'. Compound sentences like this are called conjunctions. Conjunction with two or more statements that are connected by conjunctions and. We use the symbol ^ to represent the word and, then, conjunctions 'p ^ q' represents a compound sentence 'p and q'.

EXAMPLE
Use a symbolic representation
p: Abbas, a member of PMI
q: Abbas is a Golkar cadre
Express the following compound statement using symbols:
a. Abbas is a member of the Red Cross and the Golkar Party cadres
b. Abbas, a member of PMI and he's not the Golkar Party cadres

COMPLETION
a. p ^ q
b. p ^ ~ q

Negation, Denial of Statement

Negation of a statement is a denial statement. Negation is represented using the symbol ~. Negation is often formed by adding the word 'no' in a sentence of origin. Examples are given the sentence "p: rainy day ', its negation is" ~ p: no rain today. " If the original sentence is true, its negation is false, and vice versa. Sentence truth value of negation is always contrary to the truth value of sentence of origin. Because the truth of a negation depends on the original sentence, the negation of a sentence kalmat classified as compound.

EXAMPLE
Write the sentence that represents the negation of each of the following sentences: a. Legislative candidate from Golkar Party, b. Legislative candidate was not from the Golkar Party. c. Several candidates from the Golkar party, d. All the candidates come from the democrat party, e. None of the party's legislative Hanura.

COMPLETION
a. Negation of 'legislative candidates from the Golkar Party' is 'is not a legislative candidate from Golkar Party'.
b. Negation of 'it is not a legislative candidate from Golkar Party' is 'legislative candidates from the Golkar Party'.
c. Errors often arise when asked the negation of 'a few candidates from the Golkar Party'. Many who answered 'some candidates did not come from the Golkar Party'. The statement did not reject the initial statement. The expression 'a few candidates from the Golkar Party' implies there is at least one candidate from the Golkar Party. Statements that deny this, of course, 'There are no candidates from the Golkar Party'. The statement is a negation of the initial statement.
d. Negation of 'all the candidates from the Golkar Party' is 'there is at least one candidate who did not come from the Golkar Party,' or phrase that is often used 'some candidates did not come from the Golkar Party'.
e. Negation 'No legislature of Hanura' is 'there is at least one person from the party's legislative Hanura'. When more than one interpretation at least, we can use another negation of 'some of the party's legislative Hanura.

Said some, all, and no known as quantifier, kuantor. Statement in c through e involve kuantor in it. Negation of 'all p is q' is 'some p not q'. And vice versa. And the negation 'some p is q' is 'does not exist p is q'.

Building a Compound

It is easy to determine a sentence such as "Anton donate his blood" is a statement that is true or false, simply by checking the fact whether he did or not. But not all sentences have a simple shape like that. Consider the example sentence "Anton donate his blood and has not washed his car, or he goes to the library. " That phrase is a combination of events that could occur or not on personal experience Anton. Statements like this are called compound statements. Compound statement is a statement which was formed from some simpler statement. A statement that the simplest compound can be formed by inserting the word 'not' or 'no' in a simple statement, or by combining two or more sentences using a simple statement of logic conjunctions like and, or, if - then - but only if ; and if and only if. Compound sentence 'Anton did not wash his car' comes from the more simple sentences of 'Anton wash his car'. The phrase "Anton blood donation and did not wash his car, or he went to the library," consisting of three statements, each of which can be true or false.

When did the compound sentences are true?
Before answering this, we learn first how simple sentences can be formed into sentences that are more complex sentences based on how they are linked. A compound statement can be a negation, conjunction, disjunction, conditional, or a combination thereof. Like what are they? We will discuss the following.

All should stated

All logical reasoning based on the statement. A statement is a sentence which has the only true or false value only.

EXAMPLE

a. Apple Computer Manufacturing.
b. Apple Computer Manufacturing the world's best.
c. Would you buy an IBM computer?
d. A computer thatget 2 jt discount 20% worth 1 jt .
e. I lied.

COMPLETION

a. The sentence "Apple Computer Manufacturing" is true, then, a sentence is a statement.
b. The sentence "Apple Computer Manufacturing the world's best" is an opinion. True for some and not for others, therefore, is not a sentence.
c. The phrase "Would you buy an IBM computer?" is the question. The question can also be completely wrong, therefore, this is not a statement.
d. The phrase "A computer that obtain 2 jt discount 20% worth 1 jt" is the wrong sentence. So, this is a sentence statement (20% discount from 2 jt is 1.6 jt).
e. The phrase "I lied." This sentence is a paradox, if he's right, it will be contrary to what he said. If he is wrong, then what is said is true, but it is justified as opposed to what he said. Therefore, this sentence is not a statement.

Wise Inductively

Conclusion of a valid deductive argument (which apply to specific public statement), is the conclusion / conclusion that is guaranteed. With the given premise is true, correct conclusions can be obtained. However, there is an argument that is not guaranteed given the truth even if the premise is true. Consider the following examples:

1. Dika sneeze while playing with the cat's Anton
2. Dika sneeze while playing with the cat's Tono
-------------------------------------------------- --------------------------------
So, Dika is a child who is allergic to cats

Does the conclusion is irrefutable? If the premises are true, they did support the conclusions drawn. But we can not say 100% that Dika cat allergy. Conclusion The conclusion is not indisputable. It may Dika cat allergies, but may also Dika dust allergies in cats, can also Dika is being flu.

Such reasoning is called inductive reasoning. Inductive reasoning is obtained based on some specific cases that result in general conclusions. Although sometimes we find a conclusion that is true, the conclusion of inductive reasoning was never guaranteed (not an irrefutable conclusion.) Another example of inductive reasoning is as follows:

EXAMPLE
Numbers below what after row 1, 8, 15, 22, 29, .... ?

COMPLETION
Note that we obtain a linear pattern, the pattern of arithmetic that the difference between two adjacent numbers is 7. We may respond with the next value is 36. Is our conclusion is assured? No, in a matter of no information that the sequence given an arithmetic sequence. Take for example, could have those figures are on penganggalan Monday in January AD 2001. Which means the next number is 5 (the following month.) Without more complete information, the results we get do not get guarantees from our logic, we only apply inductive reasoning, or give more than one possible solution to the problem above.