Methods of proof

Show that these three statements are equivalent where a and be are real numbers: i) a is less than b II) the average of a and b is greater than a III) the average of a and b is less than b

Recursive Definitions

I want to get a better understanding of how these problems are done. For Exercises #1-3, decide whether the sequences described are subsequences of the Fibonacci sequence, that is, their members are some or all of the members, in the right order, of the Fibonacci sequence. 1. The sequence A(n), where A(n) = (n-1)2^n-2 + 1, n ≥ 1. The first four values are 1, 2, 5, 13, which so far form a subsequence of the Fibonacci sequence. 2. The sequence C(n), where C(n) is the number of ways in which n coins can be arranged in horizontal rows with all the coins in each row touching and every coin above the bottom row touching two coins in the row below it, n ≥ 1. The first fiv... click for more

One-to-one

If f o g are one-to-one, does it follow that g is one-to-one? Justify your answer.

Relation

Let R be the relation { (1,2), (1,3),(2,3),(2,4),(3,1)} and let S be the elation { (2,1),(3,1),(3,2),(4,2)}. find SoR

Truth Values : Predicates and Quantifiers

Determine the truth value of the statement $x"y(x<= y²) (and explain your answer) if the universe of discourse for the variables consists of: a) the positive real numbers b) the integers c) the nonzero real numbers