name: date:
reading and research activity.
inductive and deductive reasoning
1. what is inductive reasoning?

2. give 2 examples of inductive reasoning

3. what is deductive reasoning

4. give two examples of deductive reasoning

5. define conjecture

6. define counterexample

Question

name:  date:
reading and research activity.
inductive and deductive reasoning
1. what is inductive reasoning?

2. give 2 examples of inductive reasoning

3. what is deductive reasoning

4. give two examples of deductive reasoning

5. define conjecture

6. define counterexample

Accepted Answer

### 1. What is inductive reasoning?
# Brief Explanations:
Inductive reasoning is a logical process where general conclusions are drawn from specific observations or examples. It involves making broad generalizations based on individual instances or patterns noticed in a set of data. For example, if you observe that the sun rises in the east every morning you've checked, you might inductively reason that the sun always rises in the east.
# Answer:
Inductive reasoning is a method of reasoning in which general conclusions are inferred from specific observations, examples, or patterns (drawing generalizations from particular instances).

### 2. Give 2 examples of inductive reasoning
# Brief Explanations:
- Example 1: You notice that every time you eat a mango, it is sweet. So, you inductively reason that all mangoes are sweet. Here, the specific instances of eating sweet mangoes lead to the general conclusion about all mangoes.
- Example 2: In your neighborhood, you see that all the dogs you've encountered (say, 5 different dogs) have four legs. From these specific observations, you inductively conclude that all dogs have four legs.
# Answer:
1. Observation: Every time I eat a mango, it is sweet. Conclusion: All mangoes are sweet.
2. Observation: The 5 dogs I've seen in my neighborhood have four legs. Conclusion: All dogs have four legs.

### 3. What is deductive reasoning
# Brief Explanations:
Deductive reasoning is a logical approach where a conclusion is derived from general principles or premises. It follows a top - down approach. If the premises are true and the logical structure is valid, the conclusion must be true. For instance, if the premise is "All humans are mortal" and another premise is "Socrates is a human", then the conclusion "Socrates is mortal" is reached deductively.
# Answer:
Deductive reasoning is a logical process in which a specific conclusion is drawn from one or more general premises (using general principles to reach a specific, valid conclusion if the premises are true).

### 4. Give two examples of deductive reasoning
# Brief Explanations:
- Example 1: Premise 1: All birds have feathers. Premise 2: A sparrow is a bird. Conclusion: A sparrow has feathers. Here, the general premise about all birds is applied to the specific case of a sparrow.
- Example 2: Premise 1: All integers ending with 0 are divisible by 10. Premise 2: 100 is an integer ending with 0. Conclusion: 100 is divisible by 10. The general rule about integers ending with 0 is used to draw a conclusion about the specific number 100.
# Answer:
1. Premise 1: All birds have feathers. Premise 2: A sparrow is a bird. Conclusion: A sparrow has feathers.
2. Premise 1: All integers ending with 0 are divisible by 10. Premise 2: 100 is an integer ending with 0. Conclusion: 100 is divisible by 10.

### 5. Define CONJECTURE
# Brief Explanations:
A conjecture is a conclusion or proposition that is proposed on the basis of incomplete evidence, as a starting point for further investigation. It is like a hypothesis that is formed inductively, based on observations or patterns, but has not yet been proven to be true (or false) with absolute certainty. For example, the Goldbach conjecture which states that every even integer greater than 2 can be expressed as the sum of two prime numbers. It is a conjecture because it has not been fully proven for all even numbers, though it holds for many observed cases.
# Answer:
A conjecture is a conclusion or proposition formulated based on incomplete evidence (observations, patterns) as a tentative hypothesis for further study (a statement proposed as true, but not yet proven).

### 6. Define COUNTEREXAMPLE
# Brief Explanations:
A counterexample is an example that disproves a general statement or conjecture. If someone claims that "All prime numbers are odd", the number 2 (which is a prime number and is even) is a counterexample because it shows that the general statement "All prime numbers are odd" is false.
# Answer:
A counterexample is an example that shows a general statement, conjecture, or proposition to be false (an instance that contradicts a universal claim).

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Question

Explanation:

1. What is inductive reasoning?

Answer:

2. Give 2 examples of inductive reasoning