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 -