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liraira [26]
3 years ago
13

You've got 60 homework problems to do and it took you 10 minutes to do eight of them. At that rate, how long will it take?

Mathematics
2 answers:
d1i1m1o1n [39]3 years ago
4 0
10 minutes : 8 problems
x minutes : 60 problems
10 * 60/8 = 150/2 = 75 minutes for 60 problems
zloy xaker [14]3 years ago
3 0
About 75 minutes because if you divide 60 by 8, you get 7.5, 7.5x10=75 so that is your answer



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a) False. A = {1}, B = {1,2} f: A ⇒ B, f(1) = 1

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d) B = {1}, A = N, f: N ⇒ {1}, f(x) = 1

Step-by-step explanation:

a) lets use A = {1}, B = {1,2} f: A ⇒ B, f(1) = 1. Here f is injective but 2 is an element of b and |f−¹({b})| = 0., not 1. This statement is False.

b) This is True. If  A were finite, then it can only be bijective with another finite set with equal cardinal, therefore, B should be finite (and with equal cardinal). If A were not finite but countable, then there should exist a bijection g: N ⇒ A, where N is the set of natural numbers. Note that f o g : N ⇒ B is a bijection because it is composition of bijections. This, B should be countable. This statement is True.

c) This is true, if f were surjective, then for every element of B there should exist an element a in A such that f(a) = b. This means that  f−¹({b}) has positive cardinal for each element b from B. since f⁻¹(b) ∩ f⁻¹(b') = ∅ for different elements b and b' (because an element of A cant return two different values with f). Therefore, each element of B can be assigned to a subset of A (f⁻¹(b)), with cardinal at least 1, this means that |B| ≤ |A|, and as a consequence, B is finite.

b) This is false, B = {1} is finite, A = N is infinite, however if f: N ⇒ {1}, f(x) = 1 for any natural number x, then f is surjective despite A not being finite.

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