College Math
Name: __________________________________
2.4 Converse, Inverse and Contrapositive
Period: __________
Given the conditional statement, write the converse, inverse, and the contrapositive in if…then form.
1. If beauty were a minute, then you would be an hour.
Identify: p: _____________________________________ q: ________________________________________
Converse (𝑞 → 𝑝): ___________________________________________________________________________
Inverse (~𝑝 → ~𝑞): __________________________________________________________________________
Contrapositive (~𝑞 → ~𝑝): ____________________________________________________________________
2. If it isn’t broke, then don’t fix it.
Identify: p: _____________________________________ q: ________________________________________
Converse: ___________________________________________________________________________
Inverse: __________________________________________________________________________
Contrapositive: ____________________________________________________________________
3. 𝑝 → ~𝑞
Converse: _____________________________
4. ~𝑝 → ~𝑞
Converse: _____________________________
Inverse: ______________________________
Inverse: ______________________________
Contrapositive: ________________________
Contrapositive: ________________________
Write each statement in the form “if p, then q.”
If p, then q
If, q
p is sufficient for q
q is necessary for p
p implies q
All p are q
p only if q
q if p
5. All integers are rational numbers.
Rule: ___________________ If p, then q form: _____________________________________________________
____________________________________________________
6. Doing crossword puzzles is sufficient for driving me crazy.
Rule: ___________________ If p, then q form: _____________________________________________________
_____________________________________________________
7. If I finish studying, I’ll go to the party.
Rule: ___________________ If p, then q form: _____________________________________________________
_____________________________________________________
8. Being in Baton Rouge is sufficient for being in Louisiana.
Rule: ___________________ If p, then q form: _____________________________________________________
_____________________________________________________
Write the statement in all forms.
9.
“If I get a job, then I will make money”
Identify: p: _______________________________________ q: ________________________________________
If p, q: _______________________________________________________________________________________
p implies q: __________________________________________________________________________________
p only if q: ___________________________________________________________________________________
p is sufficient for q: ____________________________________________________________________________
q is necessary for p: ____________________________________________________________________________
All p are q: ___________________________________________________________________________________
q if p:________________________________________________________________________________________
Identify if each statement is true or false using your biconditional rules.
10.
5 = 9 − 4 if and only if 8 + 2 = 10
11.
3 + 1 ≠ 6 if and only if 8 ≠ 8
12.
8 + 7 ≠ 15 if and only if 3 × 5 ≠ 9
13.
6 × 2 = 14 if and only if 9 + 7 ≠ 16