Chemistry & Logic Formulas and Statements

• Study notes for Quiz Review

Key Chemical Formulas

• Hydroxide: OH-
• Phosphate: PO4-3
• Nitrate: NO3-
• Carbonate: CO3-2
• Sulfite: SO3-2
• Ammonium: NH4+
• Nitrite: NO2-
• Sulfate: SO4-2
• Chloride: ClO2-
• Chlorate: ClO3-

Logic and Quantifiers

• A statement is a declarative sentence that is either true or false but not both.
• A statement can be simple or compound.

Connectives

• Compound statements get created using logical connectives such as and, or, if... then, if and only if, and not.
• If p and q are statements:
  • Negation of p (¬p) is the statement "not p". ¬p is true when p is false, and vice versa.
  • Conjunction of p and q (p ∧ q) is the statement "p and q". p ∧ q is true if both p and q are true, otherwise false.
  • Disjunction of p and q (p ∨ q) is the statement "p or q". p ∨ q is true if at least one of p or q is true, otherwise false.
  • Implication of p and q (p ⇒ q) is the statement "if p, then q". p ⇒ q is false if p is true and q is false, otherwise true. p is the hypothesis and q is the conclusion.
  • Double implication of p and q (p ⇔ q) is the statement "p if and only if q". p ⇔ q is true if both p and q are true or both are false, otherwise false.
  • The symbol ":=" means "defined as".

Examples of Statements and Connectives

• Let p = "It is raining" and q = "It is cold":
  • ¬p : "It is not raining."
  • p ∧ q : "It is raining and it is cold."
  • p ∨ q : "It is raining or it is cold."
  • p ⇒ q : "If it is raining, then it is cold."
  • p ⇔ q : "It is raining if and only if it is cold."

Tautology and Contradiction

• Tautology: A statement that is always true.
  • Ex: p ∨ ¬p
• Contradiction: A statement that is always false.