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

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

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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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