Let Z_n be the group of integers {0, 1, 2, ..., n − 1} with addition modulo n as the group operation. The number of elements in the group Z₂ × Z₃ × Z₄ that are their own inverses is __________.

Let $$f:A \to B$$ be an onto (or surjective) function, where A and B are nonempty sets. Define an equivalence relation $$\sim$$ on the set A as

$${a_1} \sim {a_2}$$ if $$f({a_1}) = f({a_2})$$,

where $${a_1},{a_2} \in A$$. Let $$\varepsilon = \{ [x]:x \in A\} $$ be the set of all the equivalence classes under $$\sim$$. Define a new mapping $$F:\varepsilon \to B$$ as

$$F([x]) = f(x)$$, for all the equivalence classes $$[x]$$ in $$\varepsilon $$.

Which of the following statements is/are TRUE?

Let X be a set and 2$$^X$$ denote the powerset of X. Define a binary operation $$\Delta$$ on 2$$^X$$ as follows:

$$A\Delta B=(A-B)\cup(B-A)$$.

Let $$H=(2^X,\Delta)$$. Which of the following statements about H is/are correct?