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

finally I have understood this question !!!

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We can take any value and compare this each expression given in option .

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in this question = is equivalent to assignment operator

and this == is comparision based operator

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

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. 

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