Inductive reasoning

Inductive reasoning

Lessons

Notes:

A conjecture is an educational guess made from the given information. Inductive reasoning is about making a conjecture that predicts the next set of patterns, or arrive at a conclusion.
  • Introduction
    Inductive Reasoning Overview:
    a)
    What are conjectures?


  • 1.
    Making a Conjecture

    Make a conjecture of the next item or number based on the information given:

    a)
    1, 3, 5, 7, 9,…

    b)
    12,13,14,15\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}

    c)
    ex 1c

    d)
    ex 1d

    e)
    ex 1e

    f)
    ex 1f


  • 2.
    Make a conjecture with the given information. Draw a figure to show that your conjecture is correct:
    a)
    ABC is a triangle and AB = BC

    b)
    ABC is a triangle and \angle B is a right angle.

    c)
    Line a a and line b b are perpendicular

    d)
    Line a a and line b b are parallel


  • 3.
    Counterexamples of Conjectures
    Determine if the following conjecture is true or false. If it is false, then find a counterexample of the conjecture:
    a)
    Given: A = (0,0), B = (0,1), C = (1,0).
    Conjecture: ABC form a right isosceles triangle.

    b)
    Given: a a is a negative integer.
    Conjecture:  a2\ a^2 is a positive integer.

    c)
    Given: AB \overline{AB} and BC \overline{BC} are parallel
    Conjecture: AB = BC

    d)
    Given: x+y10.x5 x + y \geq 10 . x \geq 5
    Conjecture: y6 y \geq 6