Introduction for simple proposition:
A simple proposition is a statement, which in the given context is either true or false but not both. The simple propositions are denoted by small letters p, q, r …
Examples:
Sum of two even integers is even integer.
`sqrt(3)` is a rational number.
Earth is flat.
7 is a prime number.
5 – 7 = -2.
Note: The statements involving opinions, question marks, exclamatory mark, command. Wish is not propositions.
Examples for simple proposition:
Logic is interesting.
What a beautiful weather!
Where are you going?
Pleas sit down.
May god bless you?
Concept - simple proposition:
Truth-value in simple proposition:
The truthiness or falsity of a proposition is called its truth-value. If a proposition is true it is denoted by “T” and if it is false it is denoted by “F.”
Example: The truth-value of
5 + 6 = 11 is “T.”
“Today is Sunday” is either “T” or “F” in the given context i.e., on a particular day it is only one of “T” or “F.”
Use of simple proposition:
Logical Connectives and Compound Propositions:
Two or more simple propositions are connected by using the words “and”, “or”, “if … then”, “if and only if”. These words or phrases are called logical connectives. Any proposition containing one or more connectives is called a compound proposition. The simple propositions occurring in a compound proposition are called its components.
Truth table:
The truth-values of the compound proposition for all possible truth-values of its components are expresses in the form of a table called truth table.
For a compound proposition with only one simple proposition, truth table consists of 2 possibilities (either T or F).
For a compound proposition with two proposition truth table consists of `2^2` = 4 possibilities. For a compound proposition with 3 propositions truth table consists of `2^3` = 8 possibilities.
Is this topic Greatest Integer Function hard for you? Watch out for my coming posts.
Example for simple proposition:
Write the following simple propositions in symbols:
An integer is even if and only if it is divisible by 2.
Solution:
Let p: An integer is even.
q: It is divisible by 2.
The given proposition is p`<=>`q.
If 6+3 =7, then 7-3=6
Solution:
Let p: 6+3=7
q: 7-3=6
Then the given proposition is p`=>`q.
A simple proposition is a statement, which in the given context is either true or false but not both. The simple propositions are denoted by small letters p, q, r …
Examples:
Sum of two even integers is even integer.
`sqrt(3)` is a rational number.
Earth is flat.
7 is a prime number.
5 – 7 = -2.
Note: The statements involving opinions, question marks, exclamatory mark, command. Wish is not propositions.
Examples for simple proposition:
Logic is interesting.
What a beautiful weather!
Where are you going?
Pleas sit down.
May god bless you?
Concept - simple proposition:
Truth-value in simple proposition:
The truthiness or falsity of a proposition is called its truth-value. If a proposition is true it is denoted by “T” and if it is false it is denoted by “F.”
Example: The truth-value of
5 + 6 = 11 is “T.”
“Today is Sunday” is either “T” or “F” in the given context i.e., on a particular day it is only one of “T” or “F.”
Use of simple proposition:
Logical Connectives and Compound Propositions:
Two or more simple propositions are connected by using the words “and”, “or”, “if … then”, “if and only if”. These words or phrases are called logical connectives. Any proposition containing one or more connectives is called a compound proposition. The simple propositions occurring in a compound proposition are called its components.
Truth table:
The truth-values of the compound proposition for all possible truth-values of its components are expresses in the form of a table called truth table.
For a compound proposition with only one simple proposition, truth table consists of 2 possibilities (either T or F).
For a compound proposition with two proposition truth table consists of `2^2` = 4 possibilities. For a compound proposition with 3 propositions truth table consists of `2^3` = 8 possibilities.
Is this topic Greatest Integer Function hard for you? Watch out for my coming posts.
Example for simple proposition:
Write the following simple propositions in symbols:
An integer is even if and only if it is divisible by 2.
Solution:
Let p: An integer is even.
q: It is divisible by 2.
The given proposition is p`<=>`q.
If 6+3 =7, then 7-3=6
Solution:
Let p: 6+3=7
q: 7-3=6
Then the given proposition is p`=>`q.
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