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# Truth tables and conditionals

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1.Give example of conditioanl where, the antecedent is false and the consequent is true, and conditional is true. Also where the conditional is false.

2. Give example of conditional where, the antecedent is false and the consequent is false and the conditional is true. Also, where the conditional is false.

3. Truth tables for the Following:
Modus ponens
Modus Tollens
Fallacy of denying the antecedent
Fallacy of affirming the consequent

4. Show by truth tables that the following are truth functionally equivalent
Not (P and Q)
Not P or not Q

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#### Solution Preview

Please see attached file. Let me know if there are any unclarities.

Truth tables and conditionals
Consider the truth table for the conditional statement (I will represent the conditional with "ïƒ ")

P Q Pïƒ Q
1. T T T
2. T F F
3. F T T
4. F F T

As we can see from the truth table, the conditional statement, Pïƒ Q is false under one valuation (i.e. assignments of truth values to P, Q) only, and this is when the antecedent is truth and the consequent is false. As such, in all conditional sentences of this type, the conditional will be true when the antecedent is false. To read this off the truth table above simply look at those rows where P, the antecedent of Pïƒ Q is false. You'll note that whenever P is false, Pïƒ Q is true.

So, in answer to your question 1, there are NO cases where a conditional statement is false when the antecedent is false.

An answer to your question 2 follows from this. Consider row 4 of the truth table. When the atoms P and Q are assigned the values 'false', the corresponding ...

#### Solution Summary

The expert examines truth tables and conditionals.

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