EasyMathematicsHigh School (11–12)Functions and Calculus › Relations and FunctionsNumerical

Let A = {1, 2, 3, 4} and B = {p, q}. How many elements do A × B and B × A each have?

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Let $A = \{1, 2, 3, 4\}$ and $B = \{p, q\}$ . How many elements do $A \times B$ and $B \times A$ each have? Are the two sets equal?

Need a reminder? The key ideaShow

$A \times B$ holds every pair $(a, b)$ , and $n(A \times B) = n(A)\,n(B)$ . A relation is any subset of $A \times B$ . On one set, a relation that is reflexive, symmetric and transitive is an equivalence relation.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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