Deductive*
Inductive reasoning makes generalizations from specific facts, and would therefore be more closely tied to forming theories.
inductive reasoning
Rodney is late every day. Therefore, Rodney will be late tomorrow as well. APEX 1.4.3
Deductive reasoning goes from a general to a specific instance. For example, if we say all primes other than two are odd, deductive reasoning would let us say that 210000212343848212 is not prime. Here is a more "classic"example of deductive reasoning. All apples are fruits All fruits grow on trees Therefore, all apples grow on trees
An example of inductive reasoning is: "Every cat I have seen has fur; therefore, all cats must have fur." This reasoning is based on specific observations and generalizing to reach a conclusion.
The product of an odd and even number will always have 2 as a factor. Therefore, it will always be even.
inductive reasoning
Examples of inductive reasoning: All the dogs we've seen are black so the next dog we see will be black; Sara is a great musician therefore her brother must also be a great musician; All the cats we've seen are brown so all cats must be brown. Examples of deductive reasoning: All cheerleaders are preppy and Lucy is a cheerleader so Lucy must be preppy; Since all teachers are smart and Karen is a teacher then Karen is smart; All basketball players are tall and Jordan is a basketball player so Jordan is tall.
inductive reasoning
If speaking in general terms, i.e. 5+2 ALWAYS equals 7 (in this case "walls and ceilings always meet at a line segment"), then it is inductive reasoning as you are going from experience and generalising to every situation with the same variables. If speaking in specific terms, i.e. all rabbits are white, Snowy's a rabbit and must therefore be white, it is deductive reasoning as you are applying a more general knowledge to a more specific situation.
Inductive logic, or inductive reasoning is any form of argument where the premises mean that the conclusion is probably correct . for example: "that ring cost me only 3 dollars. Rings that are made of gold almost always cost more than 3 dollars. Therefore that ring is not made of gold" That argument was inductive because while it is almost certainly right, it is theoretically possible that the ring is actually made of gold but was just sold for 3 dollars for some reason. Inductive logic is diffrent from deductive logic because in deductive logic if the premises are true and the conclusion logically follows the premises then there is no possible way that the conclusion could be false.
Assuming you are talking about inductive reasoning(excluding the mathematical "proof by induction"), it is the drawing of a generalized conclusion based on what you already know. For Example: All the Ice I have seen so far is cold, (previous knowledge) Therefore all ice is cold. (Generalized conclusion) Another example is: All Cats I have seen walk on four legs, therefore all cats walk on 4 legs.