Answer to Question #166367 in Discrete Mathematics for faiz

Question

Translate the following sentences and then use a short truth table to determine if the argument is valid.

If education was supported but taxes were not raised, then John was elected.

John was not elected although education was supported.

Taxes were raised only if John or Mary were elected.

So, neither education was supported nor Mary was not elected.

E = Education was supported.

J = John was elected.

M = Mary was elected.

R = Taxes were raised.

Question 5 options:

Valid

Invalid when R is true, M is true.

Invalid when R is false, M is true.

Invalid when E is true, R is false.

Invalid when R is true, M is false.

Answer 1

E = Education was supported.

J = John was elected.

M = Mary was elected.

R = Taxes were raised.

If education was supported but taxes were not raised, then John was elected.

$\Rightarrow$ E &~R=>Jb

John was not elected although education was supported.

$\Rightarrow$ ~J&E

Taxes were raised only if John or Mary were elected.

$\Rightarrow$ R=>(M or J)

So, neither education was supported nor Mary was not elected.

$\Rightarrow$ ~E=>~M

The truth table for the given statement is represented as-

Hence the given statemnt is invalid When R is true and M is false.