Download 2.2 Notes If then statements

Proofs
2.2 notes
If-Then statements and Postulates
Conditional statements (if - then):
pq =
Hypothesis (given):
Conclusion (what you are trying to prove):
Example 1: Write the statement “An angle of 40 degrees is acute” in if then form:
______________________________________________________________________________
Example 2: Identify the hypothesis and the conclusion of the conditional “If it is Tuesday, then
Phil plays tennis”
Hypothesis:
Conclusion:
The sentence " If p, then q " is a compound sentence:
o p is a sentence, which can be true or false;
o q is a sentence, which can be true or false;
o The truth of the compound sentence " If p, then q " depends on the individual truth of p
and q separately.
o A truth table can help us determine the truth of the conditional statement:
Truth table
hypothesis conclusion implication
p
q
If p, then q
Example 3: Your parents say “If you get a 90% or better in Ms. Coffey’s geometry class, then
we will buy you a car”
Converse of the conditional:
The ___________________________ p  q is ______
Example 4: Write the converse of the true conditional “An angle that measures 120 degrees is
obtuse”. Determine if the converse is true or false.
Negation:
~ p represents
Example 7: Write the negation of the statement “Ms. Coffey loves donuts”
Inverse:
The _________________________ of p  q is ________
Example 6: Write the inverse of the true conditional “A triangle has three sides”. Determine if
the contrapositive is true or false.
Contrapositive:
The _________________________ of p  q is ________
Example 7: Write the contrapositive of the true conditional “If aliens have visited Earth, then
there is life on other planets”. Determine if the contrapositive is true or false.