GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 11

Answer 1

Detailed Video Solution is here: Weekly Quiz Solutions

A. Both parts of this biconditional statement are true, so by the truth-table definition this is a true statement.
B. Both parts of this conjunction are true, so the statement is true.
C. The second part of this disjunction is true, so the statement is true.
D. The hypothesis of this conditional statement is false and the   conclusion is true, so by the truth-table definition this is a true statement. (Either of those conditions would have been enough to make the statement true.)

Answer 2

So, A,B,C,D all are true.

Answer 3

Lets represent the given data in tabular format for ease:
 

Summary of the Recent Fiscal Year

	Annual Revenue(in billion $)	Net Profit (in billion $)
Acme	138	8
Nadir	87	5
Quixote	111	13

For the sake of convenience lets call them N,A and Q respectively

a) N has smallest net profit ↔ A has the largest annual revenue
We need to see if both of these are true together or both must be false together to make the $wff$ True
Since both the atomic propositions are true so the $wff$ of option a is also true.

b)N has the lowest net profit (  5 billion dollars ) and A has the largest annual revenue so this $wff$ is also true
c) Q has the largest net profit (  13 billion dollars ) and A has the largest annual revenue so this $wff$ is also true

d)Q doesnt have  the smallest net profit so the premise or the anticedant of this $wff$ is false and we know that $ F → anything$ is always true 
So this is also true

Correct answers are a,b,c,d.