MATHEMATICS

• Linear inequalities in two variables use greater than (>), less than (<), greater

  than or equal to (≥) or less than or equal to (≤). These are inequalities that can

  be written as Ax + By < C, Ax + By ≥ C, Ax + By < C, or Ax + By ≤ C where A,

  B, and C are real numbers and A and B are both not equal to zero.
• Linear equations in two variables use the equal symbol (=). These equationscan be written in the form Ax + By = C where A, B, and C are real numbersand A and B are both not equal to zero.
• SOLID LINE for ≥ or ≤ .

  Shows the points on the line are solutions.
• BROKEN LINE for < or >. Shows the points on the

  line are NOT solutions.
• The set of first element in the ordered pairs is called the domain of the

  relation.
• The set of second element in the ordered pairs is called the range of

  the relation.
• A relation can be represented in different ways: by a list of ordered pairs,

  mapping diagram, table of values, graph, or by an equation.
• We call this as One-to-One Correspondence since for every element of x

  corresponds to an element of y.
• We call this as One-to-Many Correspondence because an element of x

  corresponds to 1 or more elements of y.
• We call this as Many-to-One Correspondence since more than 1

  element of x corresponds to an element of y.
• A function is a relation for which each value from the domain(x) is associated

  with exactly one value from the range (y). Functions can be either one to one

  or many to one.
• Independent variables are the causes because they can stand alone, while

  those in the effects are the dependent variables because it can happen if a

  certain cause has occurred.
• Function means the dependent variable is determined by the independent

  variable(s). The independent variable is denoted by x while the dependent

  variable is often designated by y. We say y is a function of x. This means y

  depends on or is determined by x.
• DOMAIN – is the set of first elements in the ordered pairs.

  Example : In the ordered pairs, {(1,2),(-1,-2),(3,4),(-3,-4)}, the

  domain is {1,-1,3,-3}.
• RANGE – is the set of second elements in the ordered pairs.

  Example : In the ordered pairs, {(1,2),(-1,-2),(3,4),(-3,-4)},
• REAL NUMBERS – is the set of rational numbers (terminating or

  repeating decimals) and irrational numbers

  (nonterminating and nonrepeating decimals).
• IIn general, LINEAR FUNCTION is a function whose domain (x-value) is

  paired with one range (y-value) only and is represented by a line.
• HYPOTHESIS – is the condition in a given statement.
• CONCLUSION – is the judgment reached by reasoning.
• PROPORTION – is the equality of two ratios.
• How do we identify if a statement is valid or invalid?

  For us to identify which statement is valid or invalid, we must follow this

  proportion,

  Hypothesis : Conclusion = Hypothesis : Conclusion
• If-Then statements are also called as CONDITIONAL STATEMENTS. The

  word “if” signals the condition or the hypothesis while the term “then” states the

  outcome or the conclusion.
• Conditional is the

  given implication.

  p → q
• Converse is

  derived when the

  hypothesis and

  conclusion in an

  implication is

  interchanged.

  q → p
• Inverse is derived

  when the

  hypothesis and

  the conclusion in

  an implication are

  negated.

  −p → −q
• Therefore, the converse of an inverse

  statement is the CONTRAPOSITIVE STATEMENT.
• Therefore, the contrapositive of a

  converse statement is the INVERSE STATEMENT.
• Therefore, the inverse of a

  contrapositive statements is the CONVERSE STATEMENT.
• Personal experience might involve at least one of the five senses of our body. A person

  might see or witness, hear, touch, smell, and taste something to state some justifications.
• Analogy is a reasoning based on similarity or likeness.
• And

  similarly, what is wrong to one is also wrong to others Intuition is a form of knowledge

  or cognition independent of experiences or reasons.
• Inductive Reasoning is the process of observing data, recognizing pattern and

  making generalization (conjecture) from these observations.
• Deductive Reasoning is the process of making use of accepted rules of logic. It

  begins with a general statement and then it is applied to prove particular cases.
• Conjecture is a generalization in mathematics based on many examples or

  illustrations.
• Argument or Logical Argument is a process of creating a new statement from one or

  more existing statements. An Argument proceeds from a set of premises to a

  conclusion by means of logical implication using a procedure called logical inference.
• DEDUCTIVE

  REASONING

  The process of reasoning

  which infer basic truth

  and/or general statements

  to arrive at a conclusion.
• INDUCTIVE REASONING

  The principle of reasoning which

  uses specific examples to arrive

  at a general rule,

  generalizations or conclusions
• Law of Detachment (Modus Ponens) p → q p ∴ q

  In symbols if p represents the hypothesis of the statement and q represents the

  conclusion,
• Law of Indirect Reasoning (Modus Tollens) p → q,~q∴~p

  In symbols if p represents the hypothesis of the statement and q represents the

  conclusion,
• Law of Syllogism (Chain Rule) p → q, q→ r ∴ p → r

  The law of syllogism is similar to the law of detachment except that it requires

  two if-then statements