Prove that the product of a non-zero rational number

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1. Prove that the product of a non-zero rational number and an irrational number is irrational.

2. Use a proof by cases to show that for any real numbers a, b and c, rnin(a, min(b, c)) = min(ntirt(a, b), c) .

3. Prove or disprove that if a and b are rational numbers then ab is also rational.

4. Prove that given a real number x, there exist unique numbers n and c such that x = n + E where n is an integer and 0 < E < 1

5. Ex. 15.1 # 5(a) (give Boolean Function in dnf only).

6. Ex. 15.2 # 4(a), 5, 8 (give Boolean Function in dnf only).

Reference no: EM13293243

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Prove that the product of a non-zero rational number : Prove that the product of a non-zero rational number and an irrational number is irrational and use a proof by cases to show that for any real numbers a, b and c, rnin(a, min(b, c)) = min(ntirt(a, b), c) .
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