Quantification Judgement Inwards Math Logic

An opened upward judgement tin dismiss live on converted into a controversy if the variable of the judgement is substituted past times a for sure constant.

For example:
Open sentence: x + four = iii for x ∈ R
If x = -1, in addition to then the higher upward judgement becomes a truthful value statement.
If x = 2, in addition to then the opened upward judgement becomes a controversy of imitation value.

Another agency to plow an opened upward judgement into a controversy is to purpose a Quantification

There are ii types of quantification inward mathematical logic, such as:

1. Universal Quantification
2. Existential Quantification

1. Universal Quantification

Universal Quantification is written amongst the symbol "∀" in addition to read "for all" or "for each". If p(x) is an opened upward judgement in addition to given a universal quantification it volition live on a revelation in addition to written (∀x) p(x) read:

• For each cost x apply the nature p.
• For all prices x has properties p.

The shape (∀x) p(x) is a declarative controversy that has a truth value to live on truthful or false, ie if it tin dismiss non live on flora x that is non p(x) in addition to then (∀x) p(x) is true. If x tin dismiss live on flora that is non p(x), in addition to then (∀x) p(x) is false.

Example of Universal Quantification

∀x existent number, x² = 1
This controversy is imitation fifty-fifty if it applies to x = - 1 or x = 1 ie 1² = 1 in addition to (1)² = 1 precisely does non apply to all x (eg x = 3, in addition to then 3² ≠ 1)

2. Existential Quantification

Existential Quantification is written amongst the symbol "∃" in addition to read "any / some" or "at to the lowest degree one". If p (x) is an opened upward judgement in addition to given an existential interrogation it volition live on a controversy in addition to written (∃x) p(x) read:

• there is x such that the applied properties p.
• some x convey properties p.
• at to the lowest degree i x past times nature p.

The shape (∃x) p(x) is a declarative controversy that has a truth value to live on truthful or imitation ie if it tin dismiss live on flora at to the lowest degree i x which is p(x) then (∃x) p(x) is true. If no x tin dismiss live on flora inward p(x) in addition to then (∃x) p(x) is false.

Example of Existential Quantification

∃x existent number, x < 1
The controversy is imitation because it tin dismiss non live on determined x the master copy release < 1.

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Referensi :

• To'Ali's mass math grouping accounting in addition to sales