proposition two

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. Propositi..

If p and q are two propositions, then the compound proposition, "if p then q" is known as conditional statement or implicatio..

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 represe..

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 ..

A Boolean algebra is a set B with two distinct elements, along with the binary operations '+' and '.' and a unary operation (') which satisfy closure property, commutative property, existence of unit element, distributive property for both the binary operations. Moreover, for all x B, t..

The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical Induction is a principle by..

A compound proposition is a tautology if it is always true for all possible combination of the truth values of its components. If a compound proposition which is always false for all possible combination of the truth values, of its components then it is called a contradict..

Two propositions (simple or compound) are said to be logically equivalent if they have identical truth values. If p is logically equivalent to q, we denote p q. We have already constructed the truth table of (~p) q in earlier class. Recall the same truth table. Truth Table fo..

A compound proposition is a tautology if it is always true for all possible combination of the truth values of its components. If a compound proposition which is always false for all possible combination of the truth values, of its components then it is called a contradiction. C..

Normally propositions are joined by 'OR', 'AND', 'NOT', 'IF .. THEN..' and 'IF AND ONLY IF' called the logical connectives . They are symbolised as follows: If two or more statements are combined by the use of words like 'AND', 'OR', 'IF AND ONLY IF ', then the resulting sta..