discrete mathematics functions

Let X = {1, 2, 3}, Y = {1,2,3,4}, and Z = {1, 2}. b. Define a function g: X -> Z that is onto but not one-to-one. c. Define a function h: X -> X that is neither one-to-one or onto. d. Define a function k: X -> X that is one-to-one and onto but is not the identity function on X.

Matrix Theory

Suppose A is diagonalizable with distinct eigenvalues... See attached file for full problem description.

Function

A function f is defined on a set of real numbers. Is f one-to-one? Please give explanation so I may understand. (see attached file for function)

One-to-one

Define F: power P({a, b, c}) -> Z as follows: for all A exist in power P({a, b, c}), F(A) = the number of elements in A. a). Is F one-to-one? Please give proof or give a counterexample. Please explain so I may understand. Thanks

Onto function

Define F: Power P({a, b, c}) -> Z as follows: for all A exist in Power P({a, b, c}), F(A) = the number of elements in A. Is F onto? Please give proof or counterexample. Please give explanation so I may understand. Thanks.

Working with discrete math functions.

A function f(x) is defined on a set of real numbers x not equal to 0 as: f(x) = (2x +1)/x. Is f(x) one to one?

Working with partial order relations in discrete math.

Let S = {0,1} and consider the partial order relation R defined on S X S X S as follows: for all ordered triples (a, b, c) and (d, e, f) in S X S X S. ( a, b, c ) R ( d, e, f ) <-> a ≤ d, b ≤ e, c ≤ f, where ≤ denotes the usual "less than or equal to" relation for real numbers. Do the maximal, ...continues

Discrete Math: Hasse diagram of a partial order relation

S = {0,1} and consider the partial order relation R defined on S X S X S as follows: for all ordered triples (a, b, c) and (d, e, f) in S X S X S. ( a, b, c ) R ( d, e, f ) <-> a ≤ d, b ≤ e, c ≤ f, where ≤ denotes the usual "less than or equal to" relation for real numbers. Please demonst ...continues

Trigonometry

The foot, F, of a hill and the base B, of a vertical tower TB, 27 metres tall, are on the same horizontal plane. From the top, T, of the tower, the angle of depression of F is 32.7 degrees. P is a point on the hill 27.5 metres away from F along the line of greatest slope. T, B, F and P all lie in the same vertical plane. The ang ...continues

Matrix Theory

See attached file for full problem description with symbols and equations. --- Definition 11.1 An orthogonal projection operator is a linear transformation such that and . Question: If W is a subspace of V, prove that P_w is an orthogonal projection. (P_w is P sub w)