Modus Tollens (indirect proof) is: (-q ^(p rightarrow q)) rightarrow -p Show the

Question

Modus Tollens (indirect proof) is: (-q ^(p rightarrow q)) rightarrow -p Show the truth table Given the conditional if (p) I go to church today then (q) -I will donate money Should the symbols and the sentences for the: Converse Inverse Contrapositive Identify the propositions (p, q, r..) and then determine what rule of inference that makes ithis valid. If it rains today, there will be no practice. If we do not practice today, then we practice tomorrow. Therefore, if it rains today we will practice tomorrow.

Explanation / Answer

1.

As all values in the last column are T, the proof is established.

2. p: I go to church today q: I will donate money

Given statement is p -> q

Converse is q -> p which is

If I will donate money I go to church today

Inverse is ~p -> ~q which is

If I do not go to church today I will not donate money

Contrapositive is ~q -> ~p which is

If I will not donate money I do not go to church today

3.

If it rains today there will be no practice. If we do not practice today then we practice tomorrow. Therefore if it rains today we will practice tomorrow.

The predicates are p: It rains today q: We practice today r: We practice tomorrow

The given statements correspond to:

p -> ~q

~q -> r

---------------------

p -> r

The rule of inference that makes this valid is the rule of hypothetical syllogism.

p q ~p ~q p -> q ~q ^ (p -> q) ~q ^ (p -> q) -> ~p T T F F T F T T F F T F F T F T T F T F T F F T T T T T

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