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Overview of related conditionals

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1 Overview of related conditionals
Unit 2: Logic and reasoning

2 p  q: “If you are thirsty, then you want a drink of water.”
True or False? If you are thirsty is the hypothesis of the conditional above. Why?

3 p  q: “If you are thirsty, then you want a drink of water.”
True or False? If you are thirsty is the hypothesis of the conditional above. Why? False. ‘If’ is never part of the hypothesis, it only points out the hypothesis.

4 Write the conclusion of the conditional statement.
p  q: If you are going to learn to drive, then you will have to take driving lessons. Write the conclusion of the conditional statement.

5 p  q: If you are going to learn to drive, then you will have to take driving lessons.
Write the conclusion of the conditional statement. you will have to take driving lessons

6 p  q: It is cloudy, if the weather forecast calls for rain.
Why is “It is cloudy” the conclusion of this conditional?

7 p  q: It is cloudy, if the weather forecast calls for rain.
Why is “It is cloudy” the conclusion of this conditional? Because there is an understood ‘then’ in front of ‘It is.’

8 Do you know your symbols? Match the symbol to the related conditional
____ 1. q  p A. Biconditional ____ 2. ~ q  ~p B. Conditional ____ 3. p  q C. Contrapositive ____ 4. ~ p  ~q D. Converse ____ 5. p  q E. Inverse

9 Do you know your symbols? Match the symbol to the related conditional
D 1. q  p A. Biconditional 2. ~ q  ~p B. Conditional 3. p  q C. Contrapositive 4. ~ p  ~q D. Converse 5. p  q E. Inverse

10 Do you know your symbols? Match the symbol to the related conditional
D 1. q  p A. Biconditional C 2. ~ q  ~p B. Conditional 3. p  q C. Contrapositive 4. ~ p  ~q D. Converse 5. p  q E. Inverse

11 Do you know your symbols? Match the symbol to the related conditional
D 1. q  p A. Biconditional C 2. ~ q  ~p B. Conditional B 3. p  q C. Contrapositive 4. ~ p  ~q D. Converse 5. p  q E. Inverse

12 Do you know your symbols? Match the symbol to the related conditional
D 1. q  p A. Biconditional C 2. ~ q  ~p B. Conditional B 3. p  q C. Contrapositive E 4. ~ p  ~q D. Converse 5. p  q E. Inverse

13 Do you know your symbols? Match the symbol to the related conditional
D 1. q  p A. Biconditional C 2. ~ q  ~p B. Conditional B 3. p  q C. Contrapositive E 4. ~ p  ~q D. Converse A 5. p  q E. Inverse

14 p  q: If you are 14, then you are too young to drive.
Write the converse of the conditional … Then evaluate it as valid, or invalid with a counterexample.

15 p  q: If you are 14, then you are too young to drive.
Write the converse of the conditional … Then evaluate it as valid, or invalid with a counterexample. If you are too young to drive, then you are 14. Invalid. Counterexample: You are 10.

16 p  q: If it’s April, then it’s time to pay income taxes.
“If it’s not April, then it’s not time to pay income taxes.” is the inverse because …

17 p  q: If it’s April, then it’s time to pay income taxes.
“If it’s not April, then it’s not time to pay income taxes.” is the inverse because … The hypothesis and conclusion of the conditional have negations (not) in them.

18 ~q  ~p: If it has no cola in it, then the soda is not RC Cola.
A) Which conditional is represented by the symbols above? B) Create the original conditional, p  q.

19 ~q  ~p: If it has no cola in it, then the soda is not RC Cola.
A) Which conditional is represented by the symbols above? Contrapositive. B) Create the original conditional, p  q. If the soda is RC Cola, then it has cola in it.

20 p  q: If it’s November 25, then it’s thanksgiving day.
Write the biconditional.

21 p  q: If it’s November 25, then it’s thanksgiving day.
Write the biconditional. It’s November 25 if and only if it’s Thanksgiving Day. It’s Thanksgiving Day iff it’s November 25. It’s November 25  it’s Thanksgiving day.

22 p  q: If it’s November 25, then it’s thanksgiving day.
Write the contrapositive.

23 p  q: If it’s November 25, then it’s thanksgiving day.
Write the contrapositive. If it’s not Thanksgiving Day, then it’s not November 25th.

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