proof

Question 1

direct proof

Answer 1

simplify LHS to get to RHS or vice versa

Question 2

proof by contradiction

Answer 2

1) identify what q implies
2) assume they are false
- find example where implication is not true
3) make implied value = p/q, then simplify
4) manipulate eg if divisible by 6 make rhs a multiple of 6
eg k=6L

Question 3

contraposition

Answer 3

show that implied part of statement is opposite form what is true by making n value equal to something that helps disprove

Question 4

induction

Answer 4

1) show statement is true for smallest value of variable (usually n=0 or n=1)
2) assume true for n=k
3) let n=k+1 and state the required result
4) manipulate new value and turn it into required result
5) state conclusoin