Logically we use connectors, these unite two propositions, that is, two sentences that can be false or true.
So we have the connective or.
Or it is a connective in which if one of the propositions is true the complete sentence is true.
If the sentence is "the car is red or blue" then if the car has one of the colors the sentence is true.
If the connective is "e" then both propositions must be true.
Paulo is big and strong.
If Paul is not big, or if Paul is not strong, the sentence is false.
We also have conditionals, conditionals determine conditions that must be satisfied.
The logical sentence that we see, we read.
if x is greater than y then y is positive
Now the next sentence reads as follows,
x is greater than y if and only if y is positive
Now, let's see some examples.
let p be a proposition and q be another proposition.
p: 9 is different from 5
q: 9 is equal to 5
Now, p is true because 9 is different from 5
q is false because 9 is not equal to 5.
But if I deny p, then p becomes false
We read 9 no it is different from 5, why, 9 is different from 5 so the denial of the truth is false.
Using the connectives.
9 is different from 5 or 9 is equal to 5.
Now, if one of the propositions is true then the sentence is true.
9 is different from 5 and 9 is equal to 5.
Now, if one of the propositions is false then the whole sentence is false
With the conditionals we can see:
This conditional determines that if the first is true and the second is false then the sentence is false, any other is true.
if 9 is different from 5 then 9 is equal to 5
which is false, but if we deny q we have.
if 9 is different from 5 then 9 is not equal to 5.
Which makes the sentence true.
In this conditional we have that if one is true and the other is false, then the sentence is false.
9 is different from 5 if and only if 9 is equal to 5.
Which is false!
9 is different from 5 if and only if 9 is not equal to 5.
Which is true!
9 is not different from 5 if and only if 9 is not equal to 5.
Which is false!
Thus, logical constructions help us to understand concepts in a rational and sequenced manner.
So we have the connective or.
Or it is a connective in which if one of the propositions is true the complete sentence is true.
If the sentence is "the car is red or blue" then if the car has one of the colors the sentence is true.
If the connective is "e" then both propositions must be true.
Paulo is big and strong.
If Paul is not big, or if Paul is not strong, the sentence is false.
We also have conditionals, conditionals determine conditions that must be satisfied.
The logical sentence that we see, we read.
if x is greater than y then y is positive
Now the next sentence reads as follows,
x is greater than y if and only if y is positive
Now, let's see some examples.
let p be a proposition and q be another proposition.
p: 9 is different from 5
q: 9 is equal to 5
Now, p is true because 9 is different from 5
q is false because 9 is not equal to 5.
But if I deny p, then p becomes false
We read 9 no it is different from 5, why, 9 is different from 5 so the denial of the truth is false.
Using the connectives.
9 is different from 5 or 9 is equal to 5.
Now, if one of the propositions is true then the sentence is true.
9 is different from 5 and 9 is equal to 5.
Now, if one of the propositions is false then the whole sentence is false
With the conditionals we can see:
This conditional determines that if the first is true and the second is false then the sentence is false, any other is true.
if 9 is different from 5 then 9 is equal to 5
which is false, but if we deny q we have.
if 9 is different from 5 then 9 is not equal to 5.
Which makes the sentence true.
In this conditional we have that if one is true and the other is false, then the sentence is false.
9 is different from 5 if and only if 9 is equal to 5.
Which is false!
9 is different from 5 if and only if 9 is not equal to 5.
Which is true!
9 is not different from 5 if and only if 9 is not equal to 5.
Which is false!
Thus, logical constructions help us to understand concepts in a rational and sequenced manner.