Changes

The definition of ''relation'' given in the next Section formally captures a concept that is actually quite familiar from everyday life.  For example, consider the relationship, involving three roles that people might play, expressed in a statement of the form "''X'' suspects that ''Y'' likes ''Z'' ".  The facts of a concrete situation could be organized in a Table like the following:

The definition of ''relation'' given in the next Section formally captures a concept that is actually quite familiar from everyday life.  For example, consider the relationship, involving three roles that people might play, expressed in a statement of the form "''X'' suspects that ''Y'' likes ''Z'' ".  The facts of a concrete situation could be organized in a Table like the following:

{| align="center" class="wikitable" style="text-align:center; width:60%"

{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:lightcyan; text-align:center; width:60%"

|+ '''Relation ''S'' : ''X'' suspects that ''Y'' likes ''Z'' '''

|+ '''Relation S : X suspects that Y likes Z'''

! Person X

! Person Y

! Person X !! Person Y !! Person Z

! Person Z

|-

|-

| Alice

| Alice || Bob || Denise

| Bob

| Denise

|-

|-

| Charles

| Charles || Alice || Bob

| Alice

| Bob

|-

|-

| Charles

| Charles || Charles || Alice

| Charles

| Alice

|-

|-

| Denise

| Denise || Denise || Denise

| Denise

| Denise

|}

|}

Each row of the Table records a fact or makes an assertion of the form "''X'' suspects that ''Y'' likes ''Z'' ".  For instance, the first row says, in effect, "Alice suspects that Bob likes Denise".  The Table represents a relation ''S'' over the set ''P'' of people under discussion:

Each row of the Table records a fact or makes an assertion of the form "''X'' suspects that ''Y'' likes ''Z'' ".  For instance, the first row says, in effect, "Alice suspects that Bob likes Denise".  The Table represents a relation ''S'' over the set ''P'' of people under discussion: