Khan.randRange(0,5) ["For integers " + katex.renderToString("a") + " and " + katex.renderToString("b, a R b") + " if and only if " + katex.renderToString("a + b") + " is even", "For integers " + katex.renderToString("a") + " and " + katex.renderToString("b, a R b") + " if and only if " + katex.renderToString("a + b") + " is odd", "For non-zero rational numbers " + katex.renderToString("a") + " and " + katex.renderToString("b, a R b") + " if and only if " + katex.renderToString("a \\times b \> 0"), "For non-zero rational numbers " + katex.renderToString("a") + " and " + katex.renderToString("b, a R b") + " if and only if " + katex.renderToString("a / b") + " is an integer", "For rational numbers " + katex.renderToString("a") + " and " + katex.renderToString("b, a R b") + " if and only if " + katex.renderToString("a - b") + " is an integer", "For rational numbers " + katex.renderToString("a") + " and " + katex.renderToString("b, a R b") + " if and only if " + katex.renderToString("| a - b | \\leq 2")] [ "True", "False", "True", "False", "True", "False" ]

Is this relation an equivalence relation?

CHOICES[CHOICESINDEX]

ANSWER[CHOICESINDEX]
  • "True"
  • "False"

A relation is an equivalence relation if it is reflextive, symmetric, and transitive.

Is the relation reflexive? That is, for every element a in the set, is (a, a) in the relation?

Is the relation symmetric? That is, for every pair a, b of distinct elements in the set, if (a, b) is in the relation, is (b, a) also in the relation?

Is the relation transitive on the set? That is, for any three elements a, b, and c, if (a, b) is in the relation and (b, c) is in the relation, then is (a, c) also in the relation?