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4 changes: 2 additions & 2 deletions src/S31.xml
Original file line number Diff line number Diff line change
Expand Up @@ -125,7 +125,7 @@ or is your instructor guilty of a falsehood?</p>

<p>As we will see when we discuss logical proofs, we can prove a conditional proposition by proving its contrapositive, which may be somewhat easier.</p>

<p>Finally, there a third variation on the proposition <m>p \rightarrow q</m>, the inverse, which we will see that has the same logical meaning as the converse.</p>
<p>Finally, there is a third variation on the proposition <m>p \rightarrow q</m>, the inverse, which we will see that has the same logical meaning as the converse.</p>

<definition xml:id="def-inverse-proposition"><title>Logical Inverse</title>
<idx><h>Inverse</h><h>Logical</h></idx>
Expand Down Expand Up @@ -267,4 +267,4 @@ For each of the following propositions, identify simple propositions, express th
</exercise>

</exercises>
</section>
</section>