What is the process of reaching a conclusion by examining specific examples?

It refers to a statement that is universal because its initial part says that a certain property is true

for all objects of a given sort, and it is existential because its second part assets the presence of

something.

Universal Existential statement

The interest computed on the basis of a 360 day year

Ordinary Interest

The total amount the borrower would need to repay on loan

Maturity Value

It is an amount where the borrower is obligated to pay before the bond is surrendered to the

borrower

Final Redemption Value

It is one whose payment depend on an event that cannot be foretold accurately

Contingent annuity

Two function are said to be equal if and only they have the same set of ordered pairs (x,y)

Equality Of Functions

It refers to denoting a set by enumerating all of its elements between braces

Set - Roster Notation

This sequence is formed by adding the proceeding two numbers , starting with 0 and 1.

Fibonacci Sequence

Population growth and bacterial decay can be modeled by the exponential growth or decay

formula

Exponential Growth Model

It refers to a statement that first part assures that a certain object exists and is universal since

its second parts says that the question fulfills a specific property for everything of a specific kind

You don't have to be Sherlock Holmes to use your powers of deductive reasoning … or would that be inductive reasoning?

What's the difference between inductive and deductive reasoning?

During the scientific process, deductive reasoning is used to reach a logical and true conclusion. Another type of reasoning, inductive, is also commonly used. People often confuse deductive reasoning with inductive reasoning; however, important distinctions separate these two pathways to a logical conclusion.

What is deductive reasoning?

Deductive reasoning, also known as deduction, is a basic form of reasoning. It starts out with a general statement, or hypothesis, and examines the possibilities to reach a specific, logical conclusion, according to Norman Herr (opens in new tab), a professor of secondary education at California State University in Northridge The scientific method uses deduction to test hypotheses and theories, which predict certain outcomes if they are correct, said Dr. Sylvia Wassertheil-Smoller (opens in new tab), a researcher and professor emerita at Albert Einstein College of Medicine. 

"We go from the general — the theory — to the specific — the observations," Wassertheil-Smoller told Live Science.

In deductive reasoning there is a first premise, then a second premise and finally an inference (a conclusion based on reasoning and evidence). A common form of deductive reasoning is the syllogism, in which two statements — a major premise and a minor premise — together reach a logical conclusion. For example, the major premise "Every A is B" could be followed by the minor premise, "This C is A." Those statements would lead to the conclusion "This C is B." Syllogisms are considered a good way to test deductive reasoning to make sure the argument is valid.

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For example, "All spiders have eight legs. A tarantula is a spider. Therefore, tarantulas have eight legs." For deductive reasoning to be sound, the hypothesis must be correct. It is assumed that the statements, "All spiders have eight legs" and "a tarantula is a spider" are true. Therefore, the conclusion is logical and true. In deductive reasoning, if something is true of a class of things in general, it is also true for all members of that class. 

Deductive conclusions are reliable provided the premises are true, according to Herr. The argument, "All bald men are grandfathers. Harold is bald. Therefore, Harold is a grandfather," is valid logically, but it is untrue because the original premise is false.

What is inductive reasoning

While deductive reasoning begins with a premise that is proven through observations, inductive reasoning extracts a likely (but not certain) premise from specific and limited observations. There is data, and then conclusions are drawn from the data; this is called inductive logic, according to the University of Illinois (opens in new tab) in Springfield.

"In inductive inference, we go from the specific to the general. We make many observations, discern a pattern, make a generalization, and infer an explanation or a theory," Wassertheil-Smoller told Live Science. "In science, there is a constant interplay between inductive inference (based on observations) and deductive inference (based on theory), until we get closer and closer to the 'truth,' which we can only approach but not ascertain with complete certainty." 

In other words, the reliability of a conclusion made with inductive logic depends on the completeness of the observations. For instance, let's say that you have a bag of coins; you pull three coins from the bag, and each coin is a penny. Using inductive logic, you might then propose that all of the coins in the bag are pennies."Even though all of the initial observations — that each coin taken from the bag was a penny — are correct, inductive reasoning does not guarantee that the conclusion will be true. 

Here's another example: "Penguins are birds. Penguins can't fly. Therefore, all birds can't fly." The conclusion does not follow logically from the statements.

Nevertheless, inductive reasoning has its place in the scientific method, and scientists use it to form hypotheses and theories. Deductive reasoning then allows them to apply the theories to specific situations.

Deductive reasoning examples

Here are some examples of deductive reasoning:

Major premise: All mammals have backbones.
Minor premise: Humans are mammals.
Conclusion: Humans have backbones.

Major premise: All birds lay eggs.
Minor premise: Pigeons are birds.
Conclusion: Pigeons lay eggs.

Major premise: All plants perform photosynthesis.
Minor premise: A cactus is a plant.
Conclusion: A cactus performs photosynthesis.

Inductive reasoning examples

Here are some examples of inductive reasoning:

Data: I see fireflies in my backyard every summer.
Hypothesis: This summer, I will probably see fireflies in my backyard.

Data: I tend to catch colds when people around me are sick.
Hypothesis: Colds are infectious.

Data: Every dog I meet is friendly. 

Hypothesis: Most dogs are usually friendly.

What is abductive reasoning

Another form of scientific reasoning that diverges from inductive and deductive reasoning is abductive. Abductive reasoning usually starts with an obviously incomplete set of observations and proceeds to the likeliest possible explanation for the data, a (opens in new tab)ccording to Butte College (opens in new tab) in Oroville, California. It is based on making and testing hypotheses using the best information available. It often entails making an educated guess after observing a phenomenon for which there is no clear explanation. 

For example, a person walks into their living room and finds torn-up papers all over the floor. The person's dog has been alone in the apartment all day. The person concludes that the dog tore up the papers because it is the most likely scenario. It's possible that a family member with a key to the apartment destroyed the papers, or it may have been done by the landlord, but the dog theory is the most likely conclusion.

Abductive reasoning is useful for forming hypotheses to be tested. Abductive reasoning is often used by doctors who make a diagnosis based on test results, and by jurors who make decisions based on the evidence presented to them.

What is the process of reaching a conclusion by applying general assumptions procedures or specific statements through a logical thought process?

What type of reasoning supports a conclusion and examining the specific examples?

What is deductive reasoning and examples?

Is a process of reaching conclusions from general to specific observation which are also used to prove a conclusion?