The Biconditional statement
If two simple statements p and q are connected by the connective 'if and only if', then the resulting compound statement is called the biconditional statement. Symbolically it is represented by p q. Example: An integer is even if and only if it i..
If two simple statements p and q are connected by the connective 'if and only if', then the resulting compound statement is called the biconditional statement. Symbolically it is represented by p q. Example: An integer is even if and only if it i..Conditional and Biconditional Statements
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 connect..
Conditional and Biconditional Statements
Logical Equivalence - 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 ta..
Logical Equivalence - 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 ta..Application of Logic in solving simple problems
Argument - An argument is a statement which assets that a given set of n compound statements p 1 ,p 2 ,..........p n yield another compound statement Q. This is denoted by where p 1 ,p 2 ,..........p n are called hypotheses or premises or assumption..
Argument - An argument is a statement which assets that a given set of n compound statements p 1 ,p 2 ,..........p n yield another compound statement Q. This is denoted by where p 1 ,p 2 ,..........p n are called hypotheses or premises or assumption..Boolean Algebra Summary
Summary - 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, the..
Summary - 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, the..Geometry And Measurement
Logical reasoning Geometric proofs Euclidean/non-Euclidean geometries Formal/informal proofs Conditional statements Pythagorean Theorem Intersection of a plane with 3-d figures Congruence, similarity, triangle inequality theorem Properties of quadrilaterals, circles, parallel li..
Logical connectives and compound statements
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 statemen..
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 statemen..Conditional statement
If p and q are two statements, then the compound statement If p then q" is called the compound statement denoted by "p q", p q is false when p is true and q is false..
If p and q are two statements, then the compound statement If p then q" is called the compound statement denoted by "p q", p q is false when p is true and q is false..The Conditional Statements
If p and q are two propositions, then the compound proposition, "if p then q" is known as conditional statement or implication. It is denoted by p q. p is called the antecedent (or hypothesis). q is called the consequent (or conclusion). Note: p q can be read as (i) If p th..
If p and q are two propositions, then the compound proposition, "if p then q" is known as conditional statement or implication. It is denoted by p q. p is called the antecedent (or hypothesis). q is called the consequent (or conclusion). Note: p q can be read as (i) If p th..What is a Simple Integration
Integrating functions with the help of some standard integrals is called simple integration. These standard integrals are derived from the basic definition of integration. Some standard theorems are used in simple integratio..
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