negation in mathematical logic

Negation and its truth table
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In this video we are going to learn negation and its truth table.
In the last video we have seen disjunction and its truth table and some of its examples. Out of these examples one of them was left for you as an exercise. I promised that I shall provide you answer in this video. The answer is given at the end this video.
So let’s begin with Negation (~):
The negation of statement p is “not p” and denoted by” ~p”. The truth value of ~p is the opposite of the truth value of the p.
While making negation pay special attention.
I shall illustrate this by an example.
Consider “6 is an even number”.
Its possible negations are
1)”6 is not even number”
Or
2) “It is false that 6 is an even number.”
But the statement “6 is an odd number.” is not negation of the given statement even though its truth value is false.
The fact is following.
The denial of the given statement is the negation of that statement.
This is strictly according to the HSC Board syllabus.
Truth table of negation.
p ~p
T F
F T
In this way we have seen negation and its truth table.
Answers of example from last video on disjunction.
2. Four or five students did not attend the lectures.
Here ‘or’ is used for represent approximate number of students and not as a connective.
Therefore, it is a simple statement. It is expressed as
P: Four or five students did not attend the lectures.
In my next video we are going to learn implication and double implication and their truth tables.
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