Define a Relation $R$ From $\mathbf { R }$ To $\mathbf { R }$

question 6

Essay

Define a relation $R$ from $\mathbf { R }$ to $\mathbf { R }$ as follows: For all $( x , y ) \in \mathbf { R } \times \mathbf { R } , ( x , y ) \in R$ if, and only if, $x = y ^ { 2 } + 1$ .
(a) Is $( 2,5 ) \in R$ ? Is $( 5,2 ) \in R$ ? Is (-3) $R$ 10? Is $10 R ( - 3 )$ ?
(b) Draw the graph of $R$ in the Cartesian plane.
(c) Is $R$ a function from $\mathbf { R }$ to $\mathbf { R }$ ? Explain.

---

Definitions:

Control Logic

The control plan for a given system; the program.

Inputs

Inputs refer to signals or data received by a system, which are then processed or used to influence operations within that system.

Outputs

Outputs refer to the data or signals sent out by a system or process, which can be in the form of information, actions, or physical quantities, as a result of its operation or processing.

Saint Peter's

A major basilica in Vatican City, an iconic example of Renaissance architecture, known for its significant artworks and as a pilgrimage site.