GATE CSE 2000 | Question: 2.26

Question

In SQL, relations can contain null values, and comparisons with null values are treated as unknown. Suppose all comparisons with a null value are treated as false. Which of the following pairs is not equivalent?

• A. $x = 5 \quad not (not (x = 5))$
• B. $x = 5 \quad x > 4$ and $x < 6,$ where $x$ is an integer
• C. $x ≠ 5 \quad not (x = 5)$
• D. none of the above

Comments

in this question = is equivalent to assignment operator

and this == is comparision based operator

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Detailed Video Solution, with Complete Analysis & Variations: https://youtu.be/zb6vXpZVo1E?t=12&feature=shared 

(MUST WATCH)

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very nice explnation @Deepak Poonia sir

Answer 1

Answer is option C.
$${\begin{array}{|c|cc|cc|cc|}\hline\\
\textbf{Value at hand}&    \textbf{Option A}& & \textbf{Option B}& &\textbf{Option C} \\\hline
   6 & \times & \times & \times & \times & \checkmark & \checkmark  \\ \hline  5 & \checkmark & \checkmark & \checkmark & \checkmark &\times & \times  \\ \hline   \text{NULL}& \times & \times & \times & \times &\color{blue} \times & \color{blue}\checkmark  \\ \hline
\end{array}}$$

Comments

@amarVashishth can oyu please explain me the options given, Like i am not able relate between null and x=5. Where does comparision with null comes in picture?

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@Aayushi, I am trying to explain option c.

Suppose all comparisons with a null value are treated as false.

now see, LHS = x !=5,  lets take x=null, => (null) !=5                  => false.

              RHS = not( x = 5) ,  => not ( null = 5)    =>> not (false) =>> true.

Now check above solution for other options..

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Can u explain about all options and their correctness, means how are they correct

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Suppose x=NULL

a) NULL=5 is false ; Not(Not(NULL=5)  => Not(Not(False))  => Not(true)   =>  false...so they are equivalent.

b) NULL=6 is false ; NULL> 4 and NULL<6 is also false so they  are also equivalent.

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Just to add a point:

Comparison with NULL value are in general unknown.
But here we are treating it to be false.

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Does anyone observe this statement comparisons with null values are treated as unknown.

And how you are concluding NULL != 5 as False.

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vijaycs

why are we taking here x=NULL?

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We’re taking x as a numeric attribute here and which can also be null. I think.

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@mani312 that's generally the case. But in the given question it is said to consider a two logic system by considering comparison with null is false. 

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Detailed Video Solution, with Complete Analysis & Variations: https://youtu.be/zb6vXpZVo1E?t=12&feature=shared 

(MUST WATCH) 

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Nice question with good explanation, thank you sir

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Sir nice question with very good explanation tahnk you sir

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Not(unknown) should be unknown

 

Right?

Answer 2

Answer: C

As (null) != 5 gives false.
But, not((null) = 5) gives not(false) gives true.

Comments

option (b)
NULL=5   False
x>4 and x<6 where x is an integer
Please explain how this evaluates to false

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in all the options, will be evaluating the pair of equations with same value of x(whether it is null or an integer) in option 'b' x is always an integer, so whatever value of x u put both x=5 and x>4 and x<6 will always give the same answer

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Yes. THANKS

Answer 3

a.null = 5   => false ,    

 not(not(null=5))  = not(not(false)) = not(true) = false

b. null = 5 => false ,

null>4 and null <6 = False and false = false

c.null ≠ 5 => false

not(null= 5)= not (false) = true

∴ option C is not eqivivalent

Answer 4

According to given question, comparison with NULL value always False, so “x ≠ 5” will be false. “x = 5” will also false and not (x = 5) = not(false) = true.
Hence, these are not equivalent pair. 

ans-C

Answer 5

SQL definition= Comparison with null value = Unknown

Given in Question = Comparison with null value = False

 

Take x= Null in every option

a-     Null=5,      not(not(x=5))

      False         not(not(False))                   --------->       True

                      Not(true)

                           False

b-      Null=5                     null>4 and null<6                      --------->       True

  False                             False        

 

C-    Null/=5                        not(null=5)

          False                            not(false)            --------->       Flase

                                                  True

Answer 6

https://youtu.be/zb6vXpZVo1E?t=12&feature=shared