Chapter 3, Problem 1ST

To determine

To express: The fact in the form of an if-then statement about $R,S$ and elements of $A$ .

Explanation of Solution

Given: The given fact is $R\subseteq S$ .

For the two relation $R$ and $S$ on set $A$ and $R\subseteq S$ , then all the elements in relation $R$ also present in $S$ .

  $\forall x,y\in A,\left(x,y\right)\in R$

Then,

  $\left(x,y\right)\in S$

The above fact in if-then format is written as,

For elements $a,b\in A$ if ${}_a{R}_b$ then ${}_a{S}_b$ .

Therefore, the fact in if-then form is written as, “For elements $a,b\in A$ if ${}_a{R}_b$ then ${}_a{S}_b$ .”