Prove that if a + b

preityk7t

preityk7t

Answered question

2022-06-14

Prove that if a + b is an irrational number, then at least one of a or b is irrational.

Answer & Explanation

robegarj

robegarj

Beginner2022-06-15Added 24 answers

The statement you're trying to prove is a , b ( a + b Q a Q  or  b Q ). This is simply the symbolic translation of the statement "for every a , b, if a + b is irrational then atleast one of a or b is irrational".
Here, the statement X is " a + b Q ", and the statement Y is " a + b Q or a Q  or  b Q ". So, the contrapositive of "for every a , b ( X Y)" is "for every a , b ( ( ¬ Y ¬ X ))", which in this case is:
For every a , b we have ( a Q and b Q a + b Q )
and this is what you argued.

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