Abstract


0011
0111
1000
1111

Only if

only if ” means “if not then not ” or .

Hypothesis

  • Also known as Antecedent
  • The part after if

Conclusion

  • Also known as Consequent
  • The part after then

Bi-conditional

  • Represented with
  • means is true if AND only if

Important

is logically equivalent to .

is a sufficient condition and necessary condition for means if and only if , or .

Sufficient Condition

  • Given
  • is a a sufficient condition for
  • If is true, is definitely true

Necessary Condition

  • Given
  • is a necessary condition for
  • must be true in order for to be claimed true

Vacuously True

  • True by default
  • When the Hypothesis is false, then statement as a whole is said to be true regardless of whether the Conclusion is true of false

Implication Law

  • Convert to

Mathematical Proof

3 Variants


Converse (相反)

001
010
101
111

Inverse (对立)

00111
01100
10011
11001

Contrapositive (逆否命题)

00111
10011
01100
11001