Practice Analogical Reasoning in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Drawing conclusions about a new situation by recognizing its structural similarity to a better-understood situation.
This is like that, so maybe what works there will work here.
Example 1
easyThe analogy between sets and logic: A \cup B (union) corresponds to p \lor q (OR), and A \cap B (intersection) corresponds to p \land q (AND). Use this analogy to conjecture a set version of De Morgan's law \neg(p \lor q) \equiv \neg p \land \neg q.
Example 2
mediumArithmetic has addition and multiplication. By analogy, what operations does set theory have, and what arithmetic laws transfer? Identify two laws that hold and one that does not.
Example 3
easyExponents satisfy a^m \cdot a^n = a^{m+n}. By analogy with functions, what does f \circ f suggest, and how does the notation f^2 fit?
Example 4
mediumIn arithmetic, the number 0 is the identity for addition (a+0=a). By analogy, identify the identity element for set union and for set intersection.