identities

If $P e^x=Q e^{-x}$ for all real values of $x$, which one of the following statements is true?

Let U = {1, 2 ,..., n}. Let A = {(x, X) | x ∈ X, X ⊆ U}. Consider the following two statements on |A|. I. |A| = n2 n–1 II. |A| = $$\sum\limits_{k = 1}^n {k\left( {\matrix{ n \cr k...

The regular expression $${0^ * }\left( {{{10}^ * }} \right){}^ * $$denotes the same set as

If the regular set $$A$$ is represented by $$A = {\left( {01 + 1} \right)^ * }$$ and the regular set $$'B'$$ is represented by $$B = \left( {{{\left( {01} \right)}^ * }{1^ * }} \ri...

Which of the following regular expression identities are true?