Q182 · Practice questionTechnology-freeSimple familiar1 mark
QUESTION 182
A student checks that is prime for and claims it is prime for every nonnegative integer. Which statement is correct?
(A)
The statement is true unless a checked value was wrong.
(B)
The checks are not a proof; n=40 gives .
(C)
Forty checked cases prove the statement.
(D)
The statement follows because the expression increases.
WORKED SOLUTION
1 markAnswer B
ANSWER
B. The checks are not a proof; n=40 gives .
Worked solution
At n=40 the expression is , which is composite. A finite list cannot prove a universal claim. An induction proof needs a valid implication from an arbitrary case to the next; numerical checks alone do not provide one.
Equivalent mathematically justified methods accepted.
Exact answers unless a decimal accuracy is specified.
Select B.
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