Computer Science - UGC NET 2021 [ Question ID = 2352 ]

Question

Which of these statements about the floor and ceiling functions are correct ? 

Statement 1 : ⌊2x⌋ = ⌊x⌋ + ⌊x + (1/2)⌋ for all real numbers x.

Statement 2 : ⌈x + y⌉ = ⌈x⌉ + ⌈y⌉ for all real numbers x and y.

1. Both Statement I and Statement II are true.
    
2. Both Statement I and Statement II are false.
    
3. Statement I is true but Statement II is false.
    
4. Statement I is false but Statement II is true.

Answer 1

Statement 1: If we put the value of x +ve or -ve number, statement 1 will be TRUE.

Statement 2: If we put the value of x and y different (eg: x= 0.5 and y= 1.5), statement 2 will be FALSE.

Hence, Option 3 "Statement I is true but statement II is false" correct.