Let x, y be real numbers. Determine which of the following statements are true. For those that are true, prove them. For those that are false, provide a counter example. For the purpose of a counter example you may assume without proof that√2, e ,π and  ln 2 are all irrational. (a) If x and y are both rational, then xy is rational. (b) If x is rational and y is irrational, then xy is rational. (c) If x is rational and y is irrational, then xy is irrational. (d) If x and y are both irrational, then xy is irrational.

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Q: Prove

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.