Select the following statements that are true. Question 4 options: If f:A→B is a function from a set A of cardinality 26 to a set B of cardinality 25, then f is not one-to-one. ∑j=1nj=C(n+1,2) The function f(x)=3x2 is an one-to-one correspondence from ℤ to ℤ. 1324t -1-101=-12-22 1+12+14+⋯+12n=2-12n
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Say that f:A->B is a function where A and B are both subsets of N. If |B| > |A|, then you can conclude which of the following? a. f is not onto b. f is not one-to-one c. the cardinality of B is greater than or equal to the cardinality of the range of f
Stark L.
Here are two important definitions related to a function f : A → B. The function f is one-to-one (1-1) if a₁ ≠ a₂ in A implies that f(a₁) ≠ f(a₂) in B. The function f is onto if, given any b ∈ B, it is possible to find an element a ∈ A for which f(a) = b. Give an example of each or state that the request is impossible: (a) f : N → N that is 1-1 but not onto. (b) f : N → N that is onto but not 1-1. (c) f : N → Z that is 1-1 and onto.
Mahajan A.
Which of the following is a synonym for a one-to-one function? bijection surjection injection rejection Question 2 Which of the following is true about the above arrow diagram? It properly defines a function but it is not a one-to-one function It properly defines a function but it is not onto It does not define a function because 3 is not mapped to any element of B It does not define a function because y is not mapped to by any element of A Question 3 Consider the function f: ℤ → ℤ, where f(n) = 2n + 1. Which of the following correctly describe domain, codomain and range? The domain and codomain are the set of all integers, but the range includes only the odd integers The domain, codomain, and range are the set of all integers The domain and range are the set of all integers, but the codomain includes only the odd integers The domain and range are the set of all integers, but the codomain includes only the even integers Question 4 Which of the following functions is a one-to-one function? f: ℤ → ℤ, where f(n) = |2n - 1| f: ℝ → ℝ, where f(x) = 3x² + 6 f: ℝ → ℝ, where f(x) = 2x + 7 f: ℤ → ℤ, where f(n) = |n| - 7 Question 5 Which of the following functions is an onto function? f: ℝ → ℝ, where f(x) = 3x + 5 f: ℤ → ℤ, where f(n) = |n - 1| f: ℝ → ℝ, where f(x) = 3x² + 6 f: ℤ → ℤ, where f(n) = 6n - 7
Adi S.
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