Answer to Question #185854 in Discrete Mathematics for MacCarthy Raymond

Question

In the following argument, determine the validity or otherwise of the

Statement:

a) “If you aren’t polite, you won’t be treated with respect. You aren’t

treated with respect. Therefore, you aren’t polite.

b) “If you play football during a thunderstorm, you’ll get hit by lightning.

You didn’t get hit by lightning. Therefore, you didn’t play football in a

thunderstorm”

Therefore, taxes are lowered.”

(i) Write out the propositional statements in the above argument?

(ii) State the premise(s) and conclusion in the argument?

(iii) Using a truth table, determine the validity of the argument?

Answer 1

a) $\Rightarrow$ The above statement is invalid because converse of the statemnt is not true.

(fallacy of converse)

(b) $\Rightarrow$ The above statement is valid because There is a contrapositive meaning of the statement.(contrapositive reasoning)

(c) $\Rightarrow$ The given statemnt is "If taxes are lowered, then income rises. Income rises. Therefore, taxes are lowered.”

$\Rightarrow$ The above statement is invalid because converse of the statemnt is not true.

(fallacy of converse)

(i) If taxes are lowered then income rises.

(ii) Premise$\Rightarrow$ taxes are lowered,

Conclusion $\Rightarrow$ income rises

(iii)Let P denote that taxes are lowered and Q denote that income rises

The given statement is P=>Q and converse is Q=>p

Truth table

If taxes are lowered, then income rises. But if income rises then Taxes are not lowered. So converse of the statement is not true So Given statement is invalid.