Conditional Statements

Equivalent Statements

Both statements are true, or both statements are false. Symbolic Form: p is true, therefore q is true. p is not true, therefore q is not true.

Contrapositive

Negate the converse. Symbolic Form: -q --> -p. If not q, then not p. Example: If tomorrow isn't Saturday, today isn't Friday.

Inverse

Negate the original conditional. Symbolic Form: -p --> -q. If not p, then not q. Example: If today isn't Friday, then tomorrow isn't Saturday.

Converse

Switch the hypothesis and the conclusion. Symbolic Form: q --> p. If q, then p. Example: If tomorrow is Saturday, today is Friday.

Hypothesis

The "if" statement. (It does not include the word "if"). Symbolic Form: p. Example: Today is Friday.

Conclusion

The "then" statement. (It does not include the word "then"). Symbolic Form: q. Example: Tomorrow is Saturday.

Negate or Negation

The opposite; from positive to negative. Symbolic Form: -. Example: Not Friday.

Conditional Statement

The original statement in if...then form. Symbolic Form: p --> q. If p, then q. Example: If today is Friday, then tomorrow is Saturday.

Biconditional Statement

When the conditional and the converse are both true; it can be written with if and only if (iff). Symbolic Form: p <--> q. Example: Today is Friday iff tomorrow is Saturday.