# Inductive/Deductive Reasoning

**Explain different between inductive reasoning and deductive reasoning.**

*Inductive reasoning: *is a type of reasoning in which we arrive at a conclusion, generalization or educated guess based on experience, observations, or patterns.

*Deductive reasoning:* (also called logical reasoning) is the logical process of using true statements to arrive at conclusion.

**2. Explain the difference between a “conjecture” and “theorem “.**

*Conjecture: *The conclusion, generalization, or educated guess which is arrived at by inductive reasoning is called a conjecture. Conjecture may or **may not be true. **A counterexample is an example which shows that a conjecture is not true (false).

*Theorem: *A theorem is a statement which can be proved using logical or deductive reasoning. A theorem cannot be proved using inductive reasoning because we can never be certain that the conclusion is **always true.**

**3. Explain the difference between an inductive ‘proof’ and deductive ‘proof’.**

**Example: **Every even number is of the form 2n, where n*E*N; Every odd number is of the form 2n-1, where n*E*N.* Consider the following statement: “When two odd number are added, their sums are always even”.*

*Inductive ‘proof’: *(Kind like showing the examples, use the true numbers to show the what the pattern is)

1+1=2; 3+5=8; 5+11=16 ……

*Deductive ‘proof’: *(use the formulas to figure out the pattern)

(2n-1)+(2m-1)=2n-1+2m-1=2(n+m)-2, so two odd number are added, their sums are always even.