Disprove that for all real numbers a and b, if a < b, then a^2 < b^2.

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Module 3: Propositional Logic & Proof Techniques.

20224m

Disprove that for all real numbers $a$ and $b$ , if $a < b$ , then $a^2 < b^2$ .

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Previous(a) Prove the following: (i) There is a real number x such that x > 1 and 2^x > x^{10}. (ii) There is an integer n such that 2n^2 - 5n + 2 is prime.Next(a) Show that p \lor (q \land r) and (p \lor q) \land (p \lor r) are logically equivalent. This is the distributive law of disjunction over conjunction.

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