Inductive reasoning and conditional statements

conjecture

is an unproven statement based on an observation

Observation: Regina wears a pink shirt on wednesday

today is wednesday

: Regina will wear a pink shirt today

conditional statement

a statement with an hypothesis and conclusion

• Today is a Wednesday, so Regina will wear a pink shirt today
  

if-then statement

a statement that has: the hypothesis has an if and then has the conclusion

• If today is a Wednesday, the Regina will wear a pink shirt today.
  

Converse

flipping the conjecture and hypothesis

• If Regina will wear a pink shirt today, then today is Wednesday

Inverse:

Negating both the hypothesis and conclusion AND flipping it around

• If today is not a Wednesday, then Regina will not wear a pink shirt toDAY

Contrapositive:

Flipping the negated hypothesis and conclusion (or write the converse then negate it)

• If Regina will not wear a pink shirt today, then today is not a Wednesday

Bi-conditional statement:

Statement that speaks truth and only the truth

• Statement that has a proven conjecture

• Iff or if and only if