Intro to Discrete maths Test Questions with Correct Answers

Intro to Discrete maths Test Questions with Correct Answers The floor function is - Answer-Assigns to the real number x the largest integer that is less than or equal to x. The Ceiling Function is - Answer-the smallest integer greater than or equal to x Compute the floor or ceiling functions, as indicated by the notion. 1. ⌊ 3/2 ⌋ 2. ⌈-1/2⌉ 3. ⌈-3/2⌉ 4. ⌊ -3/2 ⌋ - Answer-1. 1 2. 0 3. -1 4.-2 ⌈x⌉ is which function? - Answer-ceiling function ⌊ x ⌋ is which function? - Answer-floor function Which are correct for all integers n and real numbers x? 1. ⌈x⌉ = n if and only if x n = x+1 2. ⌈-x⌉ = -⌈x⌉ 3. ⌈x⌉ = n if and only if n-1x=n 4. ⌊- x ⌋ = -⌊ x ⌋ 5. ⌊ x + n⌋ = ⌊ x ⌋ + n - Answer-3. ⌈x⌉ = n if and only if n-1x=n 4. ⌊- x ⌋ = -⌊ x ⌋ 5. ⌊ x + n⌋ = ⌊ x ⌋ + n Match the function from Z to Z with it's description. 1. f(x) =x ^3 2. f(x) = x+1 3. f(x) = ⌊ x/2 ⌋ 4. f(x) = x^2+1 - Answer-1. One to one, not onto. (Every Integer is mapped to a unique value. The range consists only of perfect cubes. This is smaller than the co domain.) 2. One to one, onto (Every Integer is mapped to a unique value. The range is equal to the co-domain) 3. Not One to one, onto (0 and 1 both map to 0. The range is equal to the co-domain) 4. Not One to one, not onto (-1 and 1 both map to 2. Only positive integers are in the range.)