Test Level 2: Logical Consistency - CAT MCQ

The concept of logical connectives is used to solve the question.
1. The scene is lovely if the sky is clear.
p q
If p, then q
Conclusions:
(a) p, q ⇒ If the sky is clear, the scene is lovely.
(b) -q, -p ⇒ If the scene is not lovely, the sky is not clear.
2. The sky is never clear if it rains.
p q
If p, then q
Conclusions:
(a) p, q ⇒ If it rains, the sky is never clear.
(b) -q, -p ⇒ If the sky is clear, it will not rain.
3. Whenever it rains, I carry my umbrella with me.
p q
Whenever (if) p, then q
Conclusions:
(a) p, q ⇒ If it rains, I carry my umbrella.
(b) -q, -p ⇒ If I don't carry my umbrella, it doesn't rain.
Only option 3 is a conclusion that can be drawn from the statements, as explained above.

The question will be solved using the concept of logical connectives.
1. If Bruno, the dog, goes for walk, Anmol gives it an egg.
p q
Interpretation of 'if p, then q':
(a) p, q ⇒ If Bruno goes for walk, Anmol gives it an egg.
(b) -q, -p ⇒ If Anmol doesn't give an egg, Bruno doesn't go for walk.
2. Whenever Bruno gets an egg, it feels happy.
p q
Interpretation of 'whenever (if) p, then q':
(a) p, q ⇒ If Bruno gets an egg, it feels happy.
(b) -q, -p ⇒ If Bruno doesn't feel happy, it doesn't get an egg.
3. Whenever Bruno is excited, it wags its tail.
p q
Interpretation of 'whenever (if) p, then q':
(a) p, q ⇒ If Bruno is excited, it wags its tail.
(b) -q, -p ⇒ If Bruno doesn't wag its tail, it is not excited.
All the conclusions that could be drawn from the statements are given above. Only option 2 states one of these conclusions.

The question will be solved using the concept of logical connectives.
1. Unless you study, you will not pass the exam.
p q
Interpretation of 'unless p, then q':
(a) -p, q ⇒ If you do not study, you will not pass the exam.
(b) -q, p ⇒ You will pass the exam, if you study.
2. The exam will not take place if the student count is less than 200.
q p
Interpretation of 'if p, then q':
(a) p, q ⇒ If the student count is less than 200, the exam will not take place.
(b) -q, -p ⇒ If the exam takes place, the student count is not less than 200.
3. Either the exam will take place or the project will be evaluated.
p q
Interpretation of 'either p or q':
(a) -p, q ⇒ If the exam does not take place, the project will be evaluated.
(b) -q, p ⇒ If the project does not get evaluated, the exam will take place.
(c) p, ?
(d) q, ?
All the conclusions that could be drawn from the statements are given above. Only option 4 contains one of these conclusions.

The question will be solved using the concept of logical connectives.
1. Unless you meditate, you will not recover.
p q
Interpretation of 'unless p, then q':
(a) -p, q ⇒ If you don't meditate, you will not recover.
(b) -q, p ⇒ You recover, if you meditate.
2. If you feel well, you will perform well.
p q
Interpretation of 'if p, then q':
(a) p, q ⇒ If you feel well, you will perform well.
(b) -q, -p ⇒ If you do not perform well, you will not feel well.
3. Whenever the work is tough, you need high levels of concentration.
p q
Interpretation of 'whenever p, then q':
(a) p, q ⇒ If the work is tough, you need high levels of concentration.
(b) -q, -p ⇒ You don't need high levels of concentration, if the work is not tough.
All the conclusions that could be drawn from the given statements are mentioned above. Among the given answer choices, it is only conclusion 1 that follows.

To be called a night it has to be both dark and cloudy. If either condition is not met, it cannot be night. Clear sky means 'not cloudy.' It can`t be night because one condition (cloudy) is not met.

A is correct. Since no computers crash, and since some stocks crash, these latter stocks can't be computers.
B is incorrect. Since ALL colors are bright, no colors (glow or non-glow) can be other than bright.
C is incorrect. Since footballers that kick are dismissed, those dismissed will include footballers. We don't know whether 'some dismissed' are footballers or not.
D is correct. All those who are funny are singers. Some of the funny people are painters. This clearly implies that some singers must be painters.

Option (3) BEF
B → Death is inevitable
E → Death is also fearful
These two when read together lead to logical conclusion that death is both fearful and inevitable. Statement F conforms to the given idea though in a different way 'All fear death though everybody has to die,' therefore option (3) is the correct answer.

All sportsmen are part of the cheat circle. Cheats are divers form separate circles. Therefore, sportsmen cannot be part of the diver circle.

Marbles and toy circles intersect. Toys are part of the games circle. Therefore, marbles and games circles must also intersect.

Among the given conclusions, only 1 follows logically. It is stated that the organised people find time to rest and Sunita, in spite of being busy, is able to take time out to rest. This shows that Sunita is an organised person. So, option 1 is the correct answer.