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 -

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.