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sum, product of rational and irrational number

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Prove or disprove each of the following:
a. The sum of a rational number and an irrational number is an irrational number.
b. The product of two rational numbers is a rational number.
c. The product of two irrational numbers is an irrational number.
d. The product of a rational number and an irrational number is an irrational number.

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Solution Summary

To conclude what happens after certain operation (summation, multiplication) between rational and irrational numbers, it is important to remember that 0 is one of the rational numbers that can either disprove or prove some proposition.

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Prove or disprove each of the following:
a. The sum of a rational number and an irrational number is an irrational number.
b. The product of two rational numbers is a rational number.
c. The product of two irrational numbers is an irrational number.
d. The product of a rational number and an irrational number is an irrational number.
a. Here ...

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