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Whitepunk [10]
3 years ago
12

Give two instances in which deductive reasoning does not work.

Mathematics
1 answer:
kotegsom [21]3 years ago
3 0

Answer: Deductive reasoning does not work if the premises in which they are based are wrong or if the deduction is not based on any premises given.

Step-by-step explanation: Deductive reasoning works when we make logical assumptions or links between some given premises that are supposed to be true. One example could be assuming that all police officers work with guns, they work wearing a blue uniform and they use a black and white car. If a situation in which a person works in a blue uniform, using a black and white car and a gun is given, one can infer that this person is a police officer. But, if the premise that they work using guns is not always true, for example, you cannot say that this person is a police officer. This happens because the premise given is wrong. If one simply infers that the person in the example is a firefighter, without any logical assumptions, then it doesn't follow the deduction reasoning method.

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Step-by-step explanation:

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#2 <br> #3 <br> Need help for my discrete math class
miss Akunina [59]

For (2), start with the base case. When n = 2, we have

(n + 1)! = (2 + 1)! = 3! = 6

2ⁿ = 2² = 4

6 > 4, so the case of n = 2 is true.

Now assume the inequality holds for n = k, so that

(k + 1)! > 2ᵏ

Under this hypothesis, we want to show the inequality holds for n = k + 1. By definition of factorial, we have

((k + 1) + 1)! = (k + 2)! = (k + 2) (k + 1)!

Then by our hypothesis,

(k + 2) (k + 1)! > (k + 2) 2ᵏ = k•2ᵏ + 2ᵏ⁺¹

and k•2ᵏ ≥ 2•2² = 8, so

k•2ᵏ + 2ᵏ⁺¹ ≥ 8 + 2ᵏ⁺¹ > 2ᵏ⁺¹

which proves the claim.

Unfortunately, I can't help you with (3). Sorry!

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