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 + ...continues

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

Inverse of Modulus

Find an inverse of 2 modulo 17.

Solving Congruences

Solve the congruence of 2x ≡ 7 (mod 17)

Solving Systems of Congruences

Find all solutions to the system of congruences: x ≡ 2 (mod 3) x ≡ 1 (mod 4) x ≡ 3 (mod 5)

Fermat's Little Theorem

Use Fermat's Little Theorem to compute 3^302 mod 5, 3^302 mod 7, and 3^302 mod 11. Use your results to find 3 ^ 302 mod 385 (note 385 = 5 . 7 . 11.)

Binary and Hexadecimal Expansions

Show that the binary expansion of a positive integer can be obtained from its hexadecimal expansion by translating each hexadecimal digit into a block of four binary digits.