Practice Set on Logical connectives for CAT
1. Examine the following statements:
I. I listen to the radio only if I am bored.
II. I am never bored when I have my sister’s company.
III. Whenever I go for shopping I take my sister along.
Which one of the following conclusions can be drawn from the above statements?
a) If I am bored I listen to the radio.
b) If I am bored, I seek my sister’s company.
c) If I am not with my sister, then I’ll listen to the radio.
d) If I am not bored I do not listen to the radio.
2. If X walks less fast than Y, and Y walks as fast but not faster than Z; then, as compared to X, Z walks:
a) slower than X
b) faster than X
c) with same speed as X
d) Given data is not sufficient to determine
3. If I talk to my best friend, then I didn’t need to take a pill for headache:
A. I talked to my best friend
B. I did not need to take a pill for headache
C. I needed to take a pill for headache
D. I did not talk to my best friend.
d) AB and CD
4. “In the last T 20 Series, Virat Kohli was in great form and India won the match” is a true statement. Which of the following conclusion is correct?
a) If Virat Kohli were not in great form in the last ODI India would not have own.
b) In the last T 20 Series Virat Kohli was in great form.
c) India did not win the match.
d) India won the series.
5. “In the ensuing Panchayat polls, either OP Dhankar will get a massive mandate or dissidence in Haryana BJP intensify”. This is a True statement.
Which of following is not correct?
a) OP Dhankar got a massive mandate but dissidence in haryana BJP intensified.
b) Dissidence in Haryana BJP actually faded out.
c) OP Dhankar did not get a massive mandate in Panchayat polls.
d) Panchayat polls did not throw up clear results.
6. In cricket, if ‘how’ is the name of the batsman (on stumps) and ‘whose’ the name of the bowler, then ‘whom’ is the name of the wicket keeper. Which of the following statement represents an accurate conclusion based on the above information?
a) If who is not the batsman’s name, then whom is not the wicket keeper’s name.
b) If whom is the wicket keeper’s name, then who must be the batsman.
c) If whom is not the wicket keeper name, then who is not the batsman.
d) If whom is not the wicket keeper name, then who is not the batsman or when is not the bowler.
7. If the NDA Government moves forward in reforms process and the opposition parties support this approach then Indian economy should grow by more than eight percent annually during 2016-17 to 2020-21.
Suppose you are in 2022 and notice that Indian economy did not achieve eight percent growth, what conclusions can you draw?
a) NDA government did not last till 2022.
b) NDA government did not progress in reforms path.
c) Opposition parties continued to be hostile to reform.
d) The NDA government did not move forward on reforms or the opposition parties did not support reforms or both these happened.
8. A couple of years back a journalist wrote:
“Either CPI (M) general secretary Sitaram Yechury will evolve a new style of leadership or CPI (M) mass-base is surely going to erode’. It is a fact that Sitaram Yechury did not change his leadership style.
What conclusion can you draw from these facts, assuming that the journalist was right?
a) CPI (M) in future might lost its popular base.
b) CPI (M) has become more popular.
c) CPI (M)’s socialistic line has hit new roadblocks.
d) CPI (M) has lost its popular support but for different reasons not related to Sitaram Yechury’s leadership.
9. If Ramit attends the event then Rahul, Harshit and Vineet will also attend the event. Assuming that the above statement is true then which of the following must also be true?
a) If Ramit does not attend the event then Rahul does not attend the event.
b) If Rahul, Harshit and Vineet attend the event then Ramit will attend the event.
c) If Harshit does not attend the event then Vineet does not attend either.
d) If Rahul does not attend the event then Ramit is not going to attend the event.
10. “If exchange rate stays at present level or lower and industry performance does not deteriorate and Europe economy does not take a down turn then bull run in stock market will continue” is a true statement. Moreover, you are told that bull run did not continue. Then what conclusion will follow?
a) Exchange rate did not stay at or below the stipulated level.
b) Industry performance since then deteriorated.
c) Europe growth rate dropped.
d) At least one of (a), (b) and (c)
In this section, we will provide you the solutions to the above questions along with their explanation.
|Ques 1||Ques 2||Ques 3||Ques 4||Ques 5||Ques 6||Ques 7||Ques 8||Ques 9||Ques 10|
Option a) is incorrect, as the first statement does not state that listening radio is the only thing to do when the person gets bored.
Similarly, Option b) and c) are also incorrect.
Option d) is the logical conclusion that can be drawn from the statements.
From the given information, we get the following.
Z = Y > X
Z walks faster than X.
In a problem like this, it makes sense to mark parts (i.e., constituent propositions) with symbols.
X: In the last T 20 Series Virat Kohli was in great form.
Y: India won the match.
Then X and Y is true.
(a) Now if X is not true can we say that Y would be false? No way.
(b) Surely, X is true otherwise ‘X and Y’ cannot be true.
(c) Y cannot be false, because ‘X and Y’ is given to be true.
Hence, the statement in C cannot be correct.
(d) In ‘X and Y’, there is no mention about the series. So this statement in (d) cannot be concluded.
Let us name constituent propositions as follows:
P: In the ensuing Panchayat polls OP Dhankar will get a massive mandate.
Q: Dissidence in Haryana will intensify.
It is given that “Either P or Q” is true.
We are looking for an answer choice that is untrue.
(a) P and Q are both stated to true in this answer choice. This is impossible.
(b) This statement means that Q proved to be untrue. That is very much possible.
(c) This means that P did not come true. This is also possible. No contradiction.
(d) We cannot make any comment about this event. May or may not be true.
In this example, what you have learnt about truth table will be useful. This is and if….then’, statement where the first statement is an and-connected propositional function. The propositional function has two statements:
Statement 1 (S1): who is the name of the batsman
Statement 2 (S2): Whose is the name of the bowler