Question

Which answer choice shows that the set of irrational numbers is not closed under addition? π+(-π)=0

1/2+(-1/2)=0
π+π=2π
1/2+1/2=1​

Answer 1

(a) π + (-π) = 0

Explanation:

You want a counterexample for the statement that irrationals are closed under addition.

Closed set

A set is closed under addition if adding members of the set always results in a member of the set.

π + (-π) = 0

This shows that adding members of the set can result in a rational number. This is the counterexample you're looking for.

(1/2) + (-1/2) = 0

Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.

π + π = 2π

An example of a sum that is an element of the set. This is not a counterexample.

(1/2) +(1/2) = 1

Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.

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