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firstorder logic
True False p(t1,..tn) where t1,..,tn are terms and p is a predicate.
F1 ^ F2 conjunction  true if both F1 and F2 are true,
F1 V F2 disjunction  true if either or both are true,
F1 => F2 implication  true if F1 is false or F2 is true, F1 is the antecedent, F2 is the consequent (sometimes written with a thin arrow),
F1 <= F2 true if F1 is true or F2 is false,
F1 == F2 true if F1 and F2 are both true or both false (normally written with a three line equivalence symbol)
~F1 negation  true if f1 is false (normally written as a dash '' with a shorter vertical line hanging from its right hand end).
For all v . F universal quantification  true if F is true for all values of v (normally written with an inverted A).
Exists v . F existential quantification  true if there exists some value of v for which F is true. (Normally written with a reversed E).
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