DISCOVER PROVE: Combining Rational and Irrational Numbers Is 1 2 + 2 rational or irrational? Is 1 2 ⋅ 2 rational or irrational? Experiment with sums and products of other rational and irrational numbers. Prove the following. (a) The sum of a rational number r and an irrational number t is irrational. (b) The product of a rational number r and an irrational number t is irrational. [ Hint: For part (a), suppose that r + t is a rational number q , that is, r + t = q . Show that this leads to a contradiction. Use similar reasoning for part (b).]
DISCOVER PROVE: Combining Rational and Irrational Numbers Is 1 2 + 2 rational or irrational? Is 1 2 ⋅ 2 rational or irrational? Experiment with sums and products of other rational and irrational numbers. Prove the following. (a) The sum of a rational number r and an irrational number t is irrational. (b) The product of a rational number r and an irrational number t is irrational. [ Hint: For part (a), suppose that r + t is a rational number q , that is, r + t = q . Show that this leads to a contradiction. Use similar reasoning for part (b).]
DISCOVER PROVE: Combining Rational and Irrational Numbers Is
1
2
+
2
rational or irrational? Is
1
2
⋅
2
rational or irrational? Experiment with sums and products of other rational and irrational numbers. Prove the following.
(a) The sum of a rational number r and an irrational number t is irrational.
(b) The product of a rational number r and an irrational number t is irrational.
[Hint: For part (a), suppose that r + t is a rational number q, that is, r + t = q. Show that this leads to a contradiction. Use similar reasoning for part (b).]
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MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY