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Proposition
A statement of something to be done or considered is called proposition. You are familiar with statements such as If two straight lines intersect each other then the vertically opposite angles are equal. The angles opposite to equal sides of a triangle are equal. Proposition is..
Proposition or statement and Truth Value of a statement
A declarative sentence which is true or false but not both is called a proposition..
Proposition or statement and Truth Value of a statement
A declarative sentence which is true or false but not both is called a proposition. Truth value is the truthfulness of statement. If a statement is true its truth value is T, if a statement is false then its truth value is ..
Introduction
Geometrical figures help us to understand various geometrical concepts. When we prove geometrical propositions by logical reasoning, we draw only a rough figure and we do not need to take accurate measurements but geometrical constructions have to be drawn accurately to the give..
Conditional and Biconditional Statements
If p and q are two propositions, then the compound proposition, "if p then q" is known as conditional statement or implicatio..
Conditional and Biconditional Statements
It is already mentioned in earlier classes that compound statements of different propositions can be obtained by conjunction, disjunction and negation of propositions. We just recall these three basic logical connectivities and their truth table and subsequently we shall learn a..
Introduction
Geometrical figures help us to understand various geometrical concepts. When we prove geometrical propositions by logical reasoning, we draw only a rough figure and we do not need to take accurate measurements but geometrical constructions have to be drawn accurately to th..
Simple Construction
Introduction - Geometrical figures help us to understand various geometrical concepts. When we prove geometrical propositions by logical reasoning, we draw only a rough figure and we do not need to take accurate measurements but geometrical constructions have to be drawn accurat..
Negation
Let p be any proposition. The proposition "not p" is called the negation of p. It is denoted by ~p. [The negation of p is false if p is true and the negation of p is true if p is false] Following is the truth table for ~p..
Logical Equivalence and Duality
Two compound propositions p and q are said to be logically equivalent, if their truth values are same for each different combinations of the truth values of the components involved in them. If p and q are logically equivalent, then it is represented by p..
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