Discreet Mathematics Exercises #2

1B. 11. 12. 13. 14. Prove that two integers have the same remainder when divided by a third number, if. if and only if their di'brenee is divisible by q. Prove that a number written in the decimal system has the same remainder when divided by Q as the sum of its digits. Prove that the sum of a rational number and an irrational number is an irrational number. Prove that the sum of two rational numbers is a rational number. Prove that between any two numbers there is a rational number. Prove that between any two numbers there is an irrational number. Show that the sum of two irrational numbers can be a rational number or an irrational number