Let A = {1, 2, 3, 4} and B = {a, b, c}. Give an example of a function f: A -> B that is neither injective nor surjective.
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Let A = {1, 2, 3, 4} and B = {a, b, c}. Give an example of a function f: A -> B that is neither injective nor surjective.
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- Let A = {1, 2,3} and B = {a, b, c, d} What is the function from a to b?f:AB. A = {0, 1, 2}, B F(0) = 1, f(1) = 2, f(2) = 2 1. Is f, as described above, a function? If it is not a function, explain why. 2.If f is a function.Answer the following: a.lsfinjective? If it is not injective, explain why. {0, 1, 2} %3D b.lsf surjective? If it is not surjective, explain why. c.lsf bijective? If it is not bijective, explain why. d.Does f have an inverse? If f has an inverse, what is the domain and codomain of f? Use the name of the sets. Iff does not have an inverse, explain why. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph Arial 10pt x? X, Te Ix 田田田网 ABC - へ Ť {;} O WORDS POWERED BY !!! 田Define Functions find and find_if.
- Define a function make_derivative that returns a function: the derivative of a function f. Assuming that f is a single- variable mathematical function, its derivative will also be a single-variable function. When called with a number a, derivative will estimate the slope of f at point (a, f(a)). the Recall that the formula for finding the derivative of f at point a is: f'(a) = lim h→0 where h approaches 0. We will approximate the derivative by choosing a very small value for h. The closer h is to 0, the better the estimate of the derivative will be. def make_derivative (f): """Returns a function that approximates the derivative of f. >>> def square (x): f(a+h)-f(a) h Recall that f'(a) = (f(a + h) - f(a)) / h as h approaches 0. We will approximate the derivative by choosing a very small value for h. # equivalent to: square = lambda x: x*X return x*x >>> derivative = make_derivative (square) >>> result = derivative (3) >>> round (result, 3) # approximately 2*3 6.0 |||||| h=0.00001 "***…Rewrite the following function definitions using lambda notation: f(x) = x + 1 f(x) = x6. X is (a,b,c,d), Y is {1,2,3,4). {(a,1), (b,2), (c,2), (d,4)) is a function from X to Y.
- Write a function pythagorean that takes three integers $a$, $b$, $c$, and returns the boolean whose value is whether they constitute a Pythagorean triple, meaning that equality $a^2 + b^2 = c^2$ is satisfied. For example pythagorean(3,4,5) should return true, and pythagorean(2,4,6) should return false. This function does not output anything. You don't need to define a prototype. Test your function in your main function with the following values: Sample output1: Enter 3 numbers: 3 4 5 true Sample output2: Enter 3 numbers: 2 4 6 false C++Find the canonical representation of the following function: F(a,b) = a.a + a'.bwrite all functions f: {1,2} -> {a,b,c,d} (in two line notation) how many functions are there how many are surjective how many are injective how many are bijective please help
- Ql: The Collatz conjecture function is defined for a positive integer m as follows. (COO1) g(m) = 3m+1 if m is odd = m/2 if m is even =1 if m=1 The repeated application of the Collatz conjecture function, as follows: g(n), g(g(n)), g(g(g(n))), ... e.g. If m=17, the sequence is 1. g(17) = 52 2. g(52) = 26 3. g(26) = 13 4. g(13) = 40 5. g(40) = 20 6. g(20) = 10 7. g(10) = 5 8. g(5) = 16 9. g(16) = 8 10. g(8) = 4 11. g(4) = 2 12. g(2) = 1 Thus if m=17, apply the function 12 times in order to reach m=1. Use Recursive Function.Which functions are one-to-one? Which functions are onto? Describe the inversefunction for any bijective function.(a) f : Z → N where f is defined by f (x) = x4 + 1(b) f : N → N where f is defined by f (x) = { x/2 if x is even, x + 1 if x is odd}(c) f : N → N where f is defined by f (x) = { x + 1 if x is even, x − 1 if x is odd}let A={a,b,c,d,e} and let b the set of letters in the alphabet. Let the functions f,g,h from A to B be defined as follow