Disjunction in mathematical logic.
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In this video we are going to learn disjunction and its truth table.
In the last video we have seen conjunction and its truth table and some of its examples. Out of these examples some of them were left for you as exercise.
I promised that I shall provide you answers in this video. The answers are at the end this video.
If you are new visitor before watching this video, please watch my video on conjunction.
So let’s begin with
Disjunction(V):
A compound statement is formed by using two simple statements and connective ‘or’ is called disjunction.
In Mathematics ‘or’ is used in the inclusive sense. Thus ‘p or q’ means p or q or both p and q, where p, q are two simple statements.
The disjunction ‘p or q’ is false only when both p and q are false. In all other cases, ‘p or q’ is true.
Truth table of disjunction p V q
p q p V q
T T T
T F T
F T T
F F F
Ex. Express following in symbolic form.
1. Sanjay will go to Pune or Nasik.
2. Four or five students did not attend the lectures.
I will solve 1st example, remaining is left for you so try it, and if no possible don’t get panic. I will give the solution in my next video on negation.
Solution:
1. P: Sanjay will go to Pune.
q: Sanjay will go to Nasik.
Symbolic form is p ᴠ q.
In this way we have seen disjunction and its truth table.
Answers of examples from my last video on conjunction.
2. Anil and Sunil belongs to the same caste.
→ Here ‘and’ is combined two nouns and not two simple statements. Hence it is not used as a connective. It expressed as
p: Anil and Sunil belongs to the same caste.
3. The drug is effective though it has side effects.
→P: The drug is effective, q: The drug has side effects.
Symbolic form is p Ʌ q
4. In spite of tight security Dena bank were robbed.
→p: Dena bank has tight security. q: Dena bank were robded.
Symbolic form is p Ʌ q.
In my next video we are going to learn negation and its truth table.
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