The statement is false.
Counter-example:
When n=1, 3^(2(1))-4 = 5 which is a multiple of 5
When n=2, 3^(2(2))-4 = 65 which is not a multiple of 5
Therefore, the statement is false since it is not true for all values of n.
Counter-example is the simplest way to prove that a statement is false.
Say whether the following is true or false. If true, prove using mathematical induction. If false, give a counter-example. 3^2n-4 is a multiple of 5
2 answers
Actually the bot screwed up with its counterexample, even though it
reached the right conclusion
The AI said:
When n=2, 3^(2(2))-4 = 65 which is not a multiple of 5
it should have been:
When n=2, 3^(2(2))-4 = 76 which is not a multiple of 5
reached the right conclusion
The AI said:
When n=2, 3^(2(2))-4 = 65 which is not a multiple of 5
it should have been:
When n=2, 3^(2(2))-4 = 76 which is not a multiple of 5
2 answers