Definition of proposition
Proposition is a statement which is either true or false. There are some statements which appear to be true and false at the same time. "The area of a circle is `pi`r2 ". , is a statement or proposition whose value is true. " 6 is an odd integer" is another proposition whose value is false. Consider the question " how are you? ". This is not a proposition since it does not possess a truth value. " What time is it now ?" is another example which is not a proposition. Propositions are usually denoted by lower case letters like p, q, r, s etc.
Truth Value of a Proposition:
Proposition are statements which are either true or false. The statements which appear to be both at the same time are called paradoxes. For example consider the statement " I am a liar ". If this statement is true, then the speaker cannot be a liar. So the statement is false. If the statement is false then what the speaker says is false.Therefore the speaker is not a liar!
If a proposition is true, we say that the truth value of the proposition is True, denoted by T.
If a proposition is false, then we say that the truth value of the proposition is False, denoted by F.
Negation of a Proposition(definition Value Proposition)
" Mathematics is easy " is a proposition. Now, consider the proposition " Mathematics is not easy ". If the former is true, then the latter is false and vice-versa. Here the second proposition is called the negation of the first proposition. If p is a proposition, then the negation is denoted by the symbol ~p. The truth values of p and ~p are as follows :
p ~p
T F
F T
Compound Propositions and Connectives
A combination of two or more propositions is called a compound proposition. There are four connectives used to make compound propositions. They are summarised below.
Compound proposition connective symbol
Conjunction and `^^`
Disjunction or `vv`
Conditional if...then `|->`
Biconditional if and only if `harr`
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