1 - proof

Question 1

polynomial

Answer 1

function containing powers of x

Question 2

P=> Q

Answer 2

P implies Q

Question 3

P <=> Q

Answer 3

P is equivalent to Q
Q is true if and only if P is true

Question 4

inequality set notation

Answer 4

{ x: x>3} U { x: x<2}
{x : 2 <x <7, x EIR}
x> 3 and x<2 = { x: x € Ø}

Question 5

interval notation

Answer 5

x € (x is an element of)
x€ (a,b]
a < x <=b

Question 6

conjecture

Answer 6

a statement that has yet to be proven

Question 7

theorem

Answer 7

statement that has been proven

Question 8

proof types

Answer 8

• disproof by counter example
• proof by exhaustion
• proof by deduction

Question 9

disproof by counter example

Answer 9

find a value that shows the statement is untrue

Question 10

proof by exhaustion

Answer 10

prove its true by showing its true for all values / cases
- eg n^2 + n is always even - show for if n is a odd number and for an even number
- eg prove 41 is prime - try all prime values up to root41
- prove that when x^2 is divided by 3 there is only remained 1 or 0 - try for a value that is a multiple of 3, a multiple of 3 + 1 and a multiple of 3 +2

Question 11

proof by deduction

Answer 11

use algebra to show it as true