In each part following, either prove or disprove the converse of the given claim. If you...

 

Transcribed Image Text:

In each part following, either prove or disprove the converse of the given claim. If you prove the converse, indicate whether your proof is direct, indirect, by contradiction, or something else. If you disprove the converse, use a counterexample. (Assume known facts, such as that 2 is irrational.) In all cases, x and y are real numbers. (a) If x EQ, then 2+x Q. (b) If x Q, then 2+x Q. (c) If+y is irrational, then at least one of x and y is irrational. In each part following, either prove or disprove the converse of the given claim. If you prove the converse, indicate whether your proof is direct, indirect, by contradiction, or something else. If you disprove the converse, use a counterexample. (Assume known facts, such as that 2 is irrational.) In all cases, x and y are real numbers. (a) If x EQ, then 2+x Q. (b) If x Q, then 2+x Q. (c) If+y is irrational, then at least one of x and y is irrational.