Question

question 4
complete the following logical statement/argument:
if ab=cd and cd=ef, then ____ because ____.
○ if ab=cd and cd=ef, then cd=cd because of the symmetric property.
○ if ab=cd and cd=ef, then ab=ef because of the symmetric property.
○ if ab=cd and cd=ef, then cd=cd because of the transitive property.
○ if ab=cd and cd=ef, then ab=ef because of the transitive property.

Explanation:

The transitive property of equality states that if $a=b$ and $b=c$, then $a=c$. Here, $AB=CD$ and $CD=EF$, so applying this property gives $AB=EF$. The symmetric property applies to reversing equalities (e.g., if $a=b$ then $b=a$), which does not fit this logical step.

Answer:

If AB=CD and CD=EF, then AB=EF because of the transitive property.