- 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 nEN; Every odd number is of the form 2n-1, where nEN. 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.