basic mathematics simple and compound statements

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 ..

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 - 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..

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..

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..

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..

Truth Tables - A table is indicating the truth values of one or more statements is called a truth tabl..

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 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..

Which of the following statement(s) is/are true? I. A relationship between two variables is called simple relationship. II. When both variables increase or decrease at the same time then that relationship is called negative relationship. III. Multiple relationship exists between..