Answer to Question #173766 in Discrete Mathematics for Amo

Question

Determine the validity of the following argument:

Having a strong mathematical background is necessary and sufficient

for understanding the concepts in Information Technology. Having a 

strong mathematical background and understanding the concepts in 

Information Technology is not sufficient for you to pass all Information 

Technology exams. Therefore, if you do not pass all Information 

Technology exams it is not the case that either you did not have a strong 

mathematical background or you understood the concepts in 

information Technology.

Answer 1

Let p denote that having a strong mathematical background

and q denotes understanding the concepts in information technology

r denote to pass all information technology exam

The logical statement according to the problem are-

p$\rightarrow$ q

(p&q)$\rightarrow$ ~r

r$\rightarrow$ (~p or ~q)

The truth table is given as--

According to truth table The given statements are not satisfied.

Hence The given statement is invalid.