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 

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very nice explnation @Deepak Poonia sir

Answer 1

there are three cases included for checking every answer so we firstly we take equals to to the x =5 and secong like another value not x != 5 and then take null value so when we check this null condition on both of lhs and rhs then in rhs it gets T but lhs side its F so this is not equals here so the answer c is correct

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Answer 2

Answer: C

Because when x is NULL (and comparisons with NULL are treated as false as given in question):

• x ≠ 5 → false ( bcz comparision with null is false )

• x = 5 → false → not(x = 5) → true

So they differ when x is NULL.

Hence, Option C is not equivalent.

Answer 3

Answer: C

Given: Any comparison involving NULL is treated as FALSE.

Consider option C:

x ≠ 5        vs        NOT(x = 5)

If x = NULL:
x ≠ 5  → FALSE

x = 5  → FALSE
NOT(x = 5) → NOT(FALSE) → TRUE

Thus,

x ≠ 5 ≠ NOT(x = 5)

So, these two expressions are NOT equivalent.

Check other options:
- A: x = 5 and NOT(NOT(x = 5)) are equivalent.
- B: For integer x, x = 5 and (x > 4 AND x < 6) are equivalent. For NULL, both evaluate to FALSE.

Therefore, the correct answer is:

C. x ≠ 5 and NOT(x = 5)