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In the question below, there are three statements followed by two conclusions. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusion logically follow(s) from the given statements. Statements: 1. All keys are locks. 2. All locks are screws. 3. All doors are keys. Conclusions: I. All screws are keys. II. Some locks are keys. 
Suppose we are given n keys, m hash table slots, and two simple uniform hash functions h1 and h2. Further, suppose our hashing scheme uses h1 for the odd keys and h2 for the even keys. What is the expected number of keys in a slot? 
Statements : All the locks are keys. All the keys are bats. Some watches are bats.

Conclusions :
I. Some bats are locks.
II. Some watches are keys.
III. All the keys are locks.
The question given below consists of a statement, followed by three arguments I, II and III. You have to decide which of the arguments is/are ‘strong’ arguments is/are ‘weak’ arguments and accordingly choose your answer from the alternatives given below each question. Statement: For users, Facebook's revelation of a data breach that gave attackers access to 50 million accounts raises an important question: What happens next? For the owners of the affected accounts, and of another 40 million that Facebook considered at risk, the first order of business may be a simple one: sign back into the app. Facebook logged everyone out of all 90 million accounts in order to reset digital keys the hackers had stolen - keys normally used to keep users logged in, but which could also give outsiders full control of the compromised accounts.  Which of the following points do not capture the negligence of Facebook in the most appropriate manner? Arguments: I. What Facebook knows so far is that hackers got access to the 50 million accounts by exploiting three distinct bugs in Facebook's code that allowed them to steal those digital keys, technically known as ‘access tokens’. The company says it has fixed the bugs.  II. The hack is the latest setback for Facebook during a tumultuous year of security problems and privacy issues . So far, though, none of these issues have significantly shaken the confidence of the company's 2 billion global users.  III. One of the bugs was more than a year old and affected how the ‘View As’ feature interacted with Facebook's video uploading feature for posting ‘happy birthday’ messages. But it wasn't until mid-September that Facebook noticed an uptick in unusual activity, and not until this week that it learned of the attack.
Two statements are given, followed by four conclusions numbered I, II, III and Iv. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: No fish is a pen. All keys are pens. Conclusions: I. No fish is a pen. II. No pen is a key. III. Some pens are keys. IV. Some keys are fishes.
Statements : Some pots are keys. Some keys are locks. All keys are rings.

Conclusions :
I. Some pots are locks.
II. Some pots are not locks.
III. Some pots are rings.
IV. Some pots are not rings.
Read the given statements and conclusions carefully and choose which of the conclusions logically follows the statement. Statement: I. All keys are metal. II. Some metals are locks. Conclusion: 1. Some keys are locks. 2. Some metals are keys.
Some pins are needles. Some needles are handles. Some handles are locks. Some locks are keys. Conclusions: I. Some keys are handles II.Some handles are pins III. Some pins are keys
Statements :
All keys are locks.
All locks are bangles.
All bangles are cars.
Conclusion :
a. Some cars are locks.
b. Some bangles are keys.
c. Some cars are keys.
Statements : Some keys are staplers. Some staplers are stickers. All the stickers are pens.

Conclusions :
I. Some pens are staplers.
II. Some stickers are keys.
III. No sticker is key.
IV. Some staplers are keys.