Determine whether the statement is true or false. Prove the statement if it is true, and give a counterexample if it is false. (i) For all real numbers x and y, [x – y] = [x] – [y]. (ii) Let а, b and e be integers. If a|(bc), then alb or alc. (iii) Let m and n be integers. If m is even and n is odd, then m² – n² is odd.

Q: Suppose x is a real number. Prove that if x 2, then there is a real number y such that x =…

A:

Q: * Evaluate. 2t |4 + et| dt

A: Solution :-

Q: Prove: Let a > 0 and b > 0 then either a > 0 and b > 0 or a < 0 and b < 0. where a…

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Q: |u| ≤a is equivalent to __________ .

A: Given |u| ≤a is equivalent to __________ .

Q: Prove the statement if it is true, and give a counterexample if it is not true. a. For every real…

A: Both the subparts are solved with explanation.

Q: Find the solution to this recursive relation  an=2nan-1, a0=3

A: Given that  an=2nan-1, a0=3 To find the solution of this recursive relation

Q: Let x be a real number. If 2x2 + 1 is irrational, prove that x is irrational.

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Q: Express x XOR y with only AND, OR and NOT.

A: We can write-                    x OR y = NOT (  NOT x   AND   NOT y )

Q: (k) If x, y, and z are integers and xylz, then x|z and ylz.

A:

Q: Find x if x is not -6, and 9/12 = 5/(6+x). ______________

A: The equation 912=56+x

Q: Simplity. Assume all exponents are positive integers. 35n 45x² 2. 35n² 25x 1. 4. p²-3p-54 p-9 5.…

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Q: 4. Show that Archimedean Principle is a consequence of the assertions that every interval (a, b)…

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Q: a a + b Determine all values of a and b so that belongs to а 1 3 1 Span 1

A: We have

Q: 2. For a positive real number b, the value V-b =

A: The given expression is -b