Determine whether the following argument is valid yes or inv

Determine whether the following argument is valid (yes) or invalid (no) .

Therefore, Hugo is a physics major or Hugo is a math major.
Hugo needs to take calculus or Hugo is a math major.
If Hugo is a physics major or if Hugo is a math major, then he needs to take calculus.

Yes
No

Solution

The arguement is not valid, we can prove it using the truth table

Let us assume the conditions

A - Hugo is a physics major

B - Hugo is a maths major

C - Hugo needs to take the calculus subject

The last arguement is

(A or B) implies C

B or C

we need to infer upon the result if A or B is valid or not

Making the truth table of the list of possibilities

The third input combimnation results in a zero i.e. when hugo is not a maths major and hugo is physics major and not taking chemistry

Hence the third arguement disproves the statement