Prove that these four statements are equivalent: i)n^2 is odd, (ii) 1 - n is even, (iii) n^3 is odd , (iv) n^2 +1 is even

Prove that these four statements are equivalent: i) n^2 is odd, (ii) 1 - n is even, (iii) n^3 is odd , (iv) n^2 +1 is even

Methods of proof

Prove that the square of an even number is an even number using: a) a direct proof b) an indirect proof c) proof by contradiction

Methods of proof

Prove that if n is a positive integer, then n is even if and only if 7n+4 is even

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

A better understanding of how these problems are done.

If f 0 G are one-to-one, does it follow that g is one-to-one? Justify your answer.

If f 0 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

Predicate 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 modulo

Find an inverse of 2 modulo 17.

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

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