sets

• numbers


  The very first symbols that can be represent quantity.
• operational symbols


  +,÷, ^ and v

  connectives
• relational symbols


  =, ≤, ≥, ~

  Comparison
• grouping symbols


  ( ), { }, and [ ]

  Associate groups of numbers and operators
• variables


  Letters that represent quantities

  Pronouns
• mathematical expressions


  It is a finite group of algebraic terms and mathematical symbols combined with no equal or in equality sign.
• mathematical expressions


  Refers to objects of interesting acting as the subject in the ordinary language.
• mathematical sentence


  A sentence with complete thought, which can be regarded as true or false
• lowercase


  uppercase or lowercase: variables or counting values
• uppercase


  uppercase or lowercase: for sets and special constants
• relations


  A relation is a set of inputs and outputs, often written as ordered pairs (input, output).
• relations


  We can also represent a relation as a mapping diagram or a graph.
• function


  it is a relation in which each input has only one output.
• domain


  It is a collection of the first values in the ordered pair (Set of all input (x) values).
• range


  It is a collection of the second values in the ordered pair (Set of all output (y) values).
• logic


  is the basis of all mathematical reasoning, and of all automated reasoning.
• symbolic logic


  It is a powerful tool for analysis and communication in mathematics.

  It represents the natural language and mathematical language with symbols and variables.
• statement

  • Is an assertion which can be regarded as true or false.
  • Simple Statement
  • Compound Statement
• 2 types of statements

  simple statement and compound statement
• simple statement


  is a single statement which doesn't contain other statements as parts
• compound statement


  contains two or more statements
• truth table


  The summary of all possible truth values of a statement.
• truth table


  A mathematical table used to determine if a compound statement is true or false.
• negation


  Is the statement that contradicts p and has the opposite truth value.
• conjunction


  It is a compound statement representing the word “and”

  This statement will only be true if both p and q are true.
• conjunction


  If either p or q is false, then the conjunction is false..'
• disjunction


  it is a compound statement representing the word 'or.'

  In order for a disjunction to be true, one or both of the original statements has to be true.
• conditional


  conditional 'if-then' statement.

  They are only false when the antecedent (the 'if' part) is true, and the consequent (the 'then' part) is false.
• biconditional


  means that P and Q are equivalent.

  The double implication is true if P and Q are both true or if P and Q are both false; otherwise, the double implication is false.
• tautology


  What do you call a statement whose truth values are all true?
• contradiction


  What do you call a statement whose truth values are all false?
• antecedent


  What do you call the first statement in a conditional statement?
• consequent


  What do you call the second statement in a conditional statement?
• arguement


  All statements in an argument are called premises
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  modus ponens

  
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  modus tollens

  
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  law of syllogism

  
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  disjunctive syllogism

  
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  Fallacy of the Converse

  
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  Fallacy of the Inverse