Intermediate
Discrete Mathematics & Math
Q65 / 100
Using proof by contradiction, what assumption do you start with to prove "√2 is irrational"?
Correct! Well done.
Incorrect.
The correct answer is B) Assume √2 = a/b for integers a, b with gcd(a,b)=1, then derive that both a and b must be even, contradicting gcd(a,b)=1
B
Correct Answer
Assume √2 = a/b for integers a, b with gcd(a,b)=1, then derive that both a and b must be even, contradicting gcd(a,b)=1
Explanation
The classic contradiction proof assumes √2 is rational in lowest terms a/b, shows 2b² = a² forces a even, then b even too, contradicting gcd(a,b)=1. This pattern (assume the negation, derive a contradiction) is the template for irrationality proofs.
Progress
65/100